But private equity firms also charge fees for services like providing merger-and-acquisition advice to the portfolio companies they oversee. Many investors, arguing that they shouldn’t have to pay anything beyond the standard fee structure, began demanding that fund advisers give back a portion of those ancillary fees.

In response, fund advisers agreed to fee-sharing arrangements, in which they would reimburse investors for some ancillary fees. These reimbursements effectively offset the 1.5 percent to 2 percent management fees. In the Biomet deal, for example, the private equity firms are sharing some monitoring fees with their investors, though they declined to say how much.

There are two problems with these reimbursements. Because they can offset only the amount an investor pays in management fees, ancillary fees in excess of those payments are not shared; they are kept solely by the private equity firm. And some fund advisers have found ways to limit the amount of fees they must give back.

One example involves senior advisers hired by private equity firms to help oversee acquired companies. These advisers tend to be corporate executives with experience in a particular industry who work with the acquired companies; a former hotel executive might work with a portfolio of companies in the hospitality business, for instance, to help them run more efficiently.

Traditionally, these executives have been employed directly by the private equity firms, meaning that the firms, not their investors or the portfolio companies, have paid the executives’ salaries, which can be substantial. In other cases, they are paid by portfolio companies, which means that the salaries may be considered a fee to be partially reimbursed to the investors.

Recently, however, some private equity firms have found a way around this. Salaries of executives hired as unaffiliated contractors are not subject to reimbursements, private equity filings show, and by making these people contractors, rather than employees, firms can avoid reimbursing the investors for their costs. The private equity firms also increase profits by shifting the salary of the contractor to the payroll of portfolio companies.

Image Andrew J. Bowden, an S.E.C. official, says that “much of what we are uncovering is undetectable by even the most sophisticated investor.” Credit... Daniel Rosenbaum for The New York Times

Silver Lake Partners is a huge Silicon Valley private equity firm with $23 billion in assets, including investments in Dell, Groupon and Virtu Financial, the high-frequency trading firm. In a 2014 filing, Silver Lake noted that when it retained “senior advisers, advisers, consultants and other similar professionals who are not employees or affiliates of the adviser,” none of those payments would be reimbursed to fund investors. Silver Lake acknowledges that this creates a conflict with its investors, “because the amounts of these fees and reimbursements may be substantial and the funds and their investors generally do not have an interest in these fees and reimbursements.” Similar language is found in regulatory filings across the industry.