Exhibit 99.1

AMSURG INCREASES PROPOSAL TO MERGE WITH TEAMHEALTH; SETS DEADLINE FOR RESPONSE

Revised Proposal Offers an Additional $4.00 per TeamHealth Share in Cash

Urges TeamHealth Board to Engage; Offer to be Withdrawn on Tuesday, November 3, at 4pm ET

NASHVILLE, Tenn., November 2, 2015 – AmSurg Corp. (Nasdaq: AMSG) today announced that it has revised its proposal to combine with Team Health Holdings, Inc. (NYSE: TMH) to provide an additional $4.00 in cash per TeamHealth share. The revised proposal is 0.768 AmSurg shares plus $15.49 in cash for each TeamHealth share. The proposal has a total current value of $69.32 per TeamHealth share, or a total enterprise value of $7.6 billion, based on AmSurg’s closing stock price Friday, October 30. AmSurg first made this proposal to the Board of Directors of TeamHealth on October 24, 2015. If TeamHealth does not engage with AmSurg by 4pm ET on Tuesday, November 3, the proposal will be withdrawn.

Christopher A. Holden, President and Chief Executive Officer of AmSurg, said, “We continue to believe the proposed combination is a compelling opportunity that offers significant value to both our shareholders. After meeting with the majority of both companies’ shareholders over the past two weeks, it is clear that they are supportive of the proposed merger and agree that the time to move forward with this combination is now. We hope the TeamHealth Board will give this bold opportunity the serious consideration it deserves and will take into account input from TeamHealth shareholders. We look forward to engaging with the TeamHealth Board promptly.”

AmSurg Today sent the following letter to the TeamHealth Board of Directors:

November 2, 2015

Board of Directors

Team Health Holdings, Inc.

265 Brookview Centre Way, Ste. 400

Knoxville, TN 37919

c/o Lynn Massingale, Chairman & Mike Snow, Chief Executive Officer

Dear Lynn & Mike:

This letter is in response to our telephone conversation on Friday, October 30th, during which you relayed that the Board of Directors of TeamHealth has rejected our revised proposal of 0.768 AmSurg shares plus $15.49 in cash for each TeamHealth share. Our revised proposal represents an additional $4.00 in cash per TeamHealth share over and above our original proposal on October 12, 2015. As we have discussed,

the additional $4.00 per share included in our revised proposal is not contingent on TeamHealth taking the necessary steps to eliminate or mitigate the potential prepayment penalties associated with the financing for the IPC transaction. We ask, once again, that you reconsider engaging with us to fully evaluate this transformational opportunity to combine our two companies. Our proposal stands until 4:00pm ET on Tuesday, November 3^rd, 2015. If you do not engage with us by then, our proposal will be withdrawn.

We have a unique window of opportunity to create the best in class provider of outsourced clinical services and truly give physicians a meaningful voice in the consolidation of healthcare. The vision is clear and well understood by every stakeholder. You have been clear since our first discussion regarding concerns around timing and the potential interference with the pending IPC transaction. Let me reiterate — we would do nothing to impede the remaining steps necessary to finance and close the IPC transaction. We are fully supportive of that transaction and it is in our collective best interest for the closing to go smoothly. We firmly believe that the strategic imperative for combining our organizations outweighs risks around the integration of IPC. Consider that the potential synergies in our combination are twice the contribution of IPC today. We maintain our view that this transaction reduces shareholder risk with respect to the IPC integration. After meeting with the majority of both our shareholders over the past two weeks, we believe they are supportive of the proposed merger at a fair valuation and that the time to move forward with this combination is now.

Your Board believes TeamHealth has standalone growth prospects and value creation opportunities superior to the value offered by our proposal and the value of the combined company. We believe your shareholders should be given the opportunity to fully evaluate that proposition. It is difficult to see how any reasonable standalone financial forecast could equal or surpass the value creation to your shareholders provided by this proposal. We are proposing a true “50/50” merger, but with a substantial cash control premium to your shareholders, including approximately 30% of TeamHealth’s unaffected market equity value in cash.

Our proposal should be considered even more attractive given the recent challenges in the hospitalist and emergency services sector. We remain supportive of the IPC transaction, despite the challenging quarter it just announced. That said, we believe the recent trading performance in the hospitalist and emergency services sectors, as well as the recent performance of IPC specifically, have reduced the likely unaffected trading price of TeamHealth stock. Absent our public proposal, TeamHealth would likely have traded down with a reasonable assumption of a ~5% discount or ~$49 (Mednax and Envision Healthcare declined 12% and 22%, respectively) to its unaffected price of $52.50, this revised proposal would represent a ~40% “headline premium.” Given this dynamic, we believe our proposal is reflective of two increases in value: 1) affirmation of our prior proposal in light of the decline in valuation for the hospitalist and emergency services sectors as well as IPC’s challenging quarter, and 2) our increased proposal with $4.00 of additional cash. We also believe the stock portion of our proposal is further strengthened by the fact that AmSurg exceeded consensus estimates for the third quarter by 10% versus the relatively weaker financial performance of the physician services sector (TeamHealth, IPC, Mednax and Envision Healthcare) and healthcare providers broadly.

Your Board indicated that if TeamHealth were to engage in a dialogue with AmSurg at some point in the future, such engagement would not occur unilaterally, but as part of a broader sale process involving multiple parties. We believe that the public nature of this proposal — as well as the proposed 50% ongoing interest by TeamHealth shareholders in the combined company — provide ample flexibility for TeamHealth to engage in a dialogue with AmSurg without conducting a lengthy auction process.

We remain very excited by the prospect of combining our businesses and believe the combination of TeamHealth and AmSurg is compelling strategically and financially. Our Board of Directors and management team are committed to working with you to pursue a transaction expeditiously.

We hope you and your Board will give this bold opportunity the serious consideration it deserves and will take into account input from TeamHealth shareholders, many of whom have expressed to us support for a transaction.

We look forward to hearing from you promptly.

Yours truly,

Christopher Holden

President and Chief Executive Officer

About AmSurg Corp.

AmSurg’s Ambulatory Services Division acquires, develops and operates ambulatory surgery centers in partnership with physicians throughout the U.S. AmSurg’s Physician Services Division, Sheridan, provides outsourced physician services in multiple specialties to hospitals, ASCs and other healthcare facilities throughout the U.S., primarily in the areas of anesthesiology, children’s services, emergency medicine and radiology. Through these businesses as of June 30, 2015, AmSurg owned and operated 250 ASCs in 34 states and provided physician services to more than 350 healthcare facilities in 27 states. AmSurg has partnerships with, or employs, over 5,000 physicians in 38 states and the District of Columbia.

Forward-Looking Statements

This press release includes forward-looking statements within the meaning of Section 27A of the Securities Act and Section 21E of the Securities Exchange Act of 1934, as amended. These forward-looking statements include, but are not limited to, statements regarding AmSurg’s proposed business combination transaction with TeaHealth (including financing of the proposed transaction and the benefits, results, effects and timing of a transaction), all statements regarding AmSurg’s (and AmSurg’s and TeamHealth’s combined) expected future financial position, results of operations, cash flows, financing plans, business strategy, budgets, capital expenditures, competitive positions, growth opportunities, plans and objectives of management, and statements containing the words such as “anticipate,” “approximate,” “believe,” “plan,” “estimate,” “expect,” “project,” “could,” “would,” “should,” “will,” “intend,” “may,” “potential,” and other similar expressions. Statements in this press release concerning the business outlook or future economic performance, anticipated profitability, revenues, expenses or other financial items, and service line growth of AmSurg (and the combined businesses of AmSurg and TeamHealth), together with other statements that are not historical facts, are forward-looking statements that are estimates reflecting the best judgment of AmSurg based upon currently available information.

Such forward-looking statements are inherently uncertain, and shareholders and other potential investors must recognize that actual results may differ materially from AmSurg’s expectations as a result of a variety of factors, including, without limitation, those discussed below. Such forward-looking statements are based upon management’s current expectations and include known and unknown risks, uncertainties and other factors, many of which AmSurg is unable to predict or control, that may cause AmSurg’s actual results, performance or plans with respect to TeamHealth, to differ materially from any future results, performance or plans expressed or implied by such forward-looking statements. These statements involve risks, uncertainties and other factors discussed below and detailed from time to time in AmSurg’s filings with the Securities and Exchange Commission (the “SEC”).

Risks and uncertainties related to the proposed transaction with TeamHealth include, but are not limited to, uncertainty as to whether AmSurg will further pursue, enter into or consummate the transaction on the terms set forth in the proposal or on other terms, potential adverse reactions or changes to business relationships resulting from the announcement or completion of the transaction, uncertainties as to the timing of the transaction, adverse effects on AmSurg’s stock price resulting from the announcement or consummation of the transaction or any failure to complete the transaction, competitive responses to the announcement or consummation of the transaction, the risk that regulatory, licensure or other approvals and financing required for the consummation of the transaction are not obtained or are obtained subject to terms and conditions that are not anticipated, costs and difficulties related to the integration of TeamHealth’s businesses and operations with AmSurg’s businesses and operations, the inability to obtain, or delays in obtaining, cost savings and synergies from the transaction, unexpected costs, liabilities, charges or expenses resulting from the transaction, litigation relating to the transaction, the inability to retain key personnel, and any changes in general economic and/or industry specific conditions.

In addition to the factors set forth above, other factors that may affect AmSurg’s plans, results or stock price including, but not limited to, the following risks: AmSurg may face challenges managing its physician services division as a new business and may not realize anticipated benefits; AmSurg may become subject to investigations by federal and state entities and unpredictable impacts of the Health Reform Law; AmSurg may not be able to successfully maintain effective internal controls over financial reporting; AmSurg may not be able to implement its business strategy, manage the growth in its business, and integrate acquired businesses; AmSurg’s substantial indebtedness and restrictions in its debt instruments could adversely affect its business or its ability to implement its growth strategy, or limit its ability to react to changes in the economy or its industry; AmSurg may not generate sufficient cash to service its indebtedness; regulatory changes may obligate AmSurg to buy out interests of physicians who are minority owners of its surgery centers; AmSurg may not be able to successfully maintain its information systems and processes, implement new systems and processes, and maintain the security of those systems and processes; AmSurg may be subject to litigation and investigations and liability claims for damages and other expenses not covered by insurance; AmSurg may be required to write-off a portion of its intangible assets; payments from third-party payors, including government healthcare programs, may decrease or not increase as AmSurg’s costs increase; there may be adverse developments affecting the medical practices of AmSurg’s physician partners; AmSurg may not be able to maintain favorable relations with its physician partners; AmSurg may not be able to grow its ambulatory services revenue by increasing procedure volume while maintaining operating margins and profitability at its existing surgery centers; AmSurg may not be able to compete for physician partners, managed care contracts, patients and strategic relationships; adverse weather and other factors beyond AmSurg’s control may affect its business; AmSurg may be adversely impacted by changes in patient volume and patient mix; several client relationships generate a significant portion of AmSurg’s physician services revenues; AmSurg’s physician services contracts may be cancelled or not renewed or AmSurg may not be able to enter into additional contracts under terms acceptable to it; reimbursement rates, revenue and profit margin under AmSurg’s fee-for-service physician services payor contracts may decrease; AmSurg may not be able to timely or accurately bill its services; AmSurg may not be able to enroll its physician services providers in the Medicare and Medicaid programs on a timely basis; AmSurg’s strategic partnerships with healthcare providers may not be successful; AmSurg may not be able to successfully recruit and retain physicians, nurses and other clinical providers; AmSurg may not be able to accurately assess the costs it will incur under new contracts; AmSurg’s margins may be negatively impacted by cross-selling to existing clients or selling bundled services to new clients; AmSurg may not be able to enforce non-compete agreements with its physicians and other clinical employees in some jurisdictions; there may be unfavorable changes in regulatory, economic and other conditions in the states where AmSurg operates; legislative or regulatory action may make AmSurg’s captive insurance company arrangement less feasible or otherwise reduce its profitability; AmSurg’s reserves with respect to its losses covered

under its insurance programs may not be sufficient; and the other risk factors are described in AmSurg’s Annual Report on Form 10-K for the fiscal year ended December 31, 2014, as updated by other filings with the Securities and Exchange Commission. Consequently, actual results, performance or developments may differ materially from the forward-looking statements included above. AmSurg disclaims any intent or obligation to update these forward-looking statements.

AmSurg has provided information in this press release to compute certain non-GAAP measurements for specified periods. A reconciliation of the non-GAAP measurements to the GAAP measurements is included this press release and on AmSurg’s web site, www.amsurg.com, by following the link to Investors.

Additional Information

This press release is provided for informational purposes only and does not constitute an offer to purchase or the solicitation of an offer to sell any securities. Subject to future developments, AmSurg may file a registration statement and/or tender offer documents with the SEC in connection with a possible business combination transaction with TeamHealth. AmSurg and TeamHealth shareholders should read those filings, and any other filings made by AmSurg with the SEC in connection with a possible business combination, if any, as they will contain important information. Those documents, if and when filed, as well as AmSurg’s other public filings with the SEC, may be obtained without charge at the SEC’s website at www.sec.gov and at AmSurg’s website at www.amsurg.com.