These entities, he cautioned, should avoid engaging in “private inurement,” or providing excessive benefit to a person who is close to or has a controlling interest in a nonprofit  though tax law says nothing about how much is too much.

Even newer models are evolving. Several states have passed legislation that permits the creation of so-called LC3 companies, which can raise money from traditional capital markets but place social benefit ahead of profit, and B Corporations, which are certified based on their ability to demonstrate that their business produces certain social goods. But Will Rosenzweig, a founder of the specialty tea company Republic of Tea and now the managing director of Physic Ventures, another firm that looks to invest in companies that bring social benefit, expressed skepticism of the new models. “I think you really have to make a choice and be a business or be a nonprofit,” he said. “It’s hard to be both.”

Concerns about the hybrid model surfaced in a very public way earlier this year when a tiny nonprofit in Seattle, Unitus, abruptly announced that it was letting go almost all of its employees and no longer accepting donations.

The award-winning nonprofit had helped commercialize the microfinance industry through its profit-making venture capital arm, which had made investments in several microfinance banks that were poised to go public, generating huge returns for investors, some of whom were Unitus board members.

There are, of course, examples of pushmi-pullyus whose two heads have learned to collaborate. In a structure reminiscent of mutual insurers of yore, members of the nonprofit Freelancers Union own the profit-making Freelancers Insurance Company, and both are affiliated with the charity Working Today. Board members of the nonprofit sit on the board of the profit-making company, and employees of both determine how expenses are allocated among the three organizations.

“It’s complicated but necessary,” said Sara Horowitz, who often jokes that she is the lowest-paid chief executive of an insurance company in America. “The structure ensures that there is no way that Freelancer’s Union could be sold for the benefit of any individuals or that the nonprofit could be abused for the benefit of the company.”