When Anthropic gathered public-market investors recently to whet their appetites for its initial public offering, executives highlighted ballooning revenues and rapidly advancing technology. On Sunday, the company unveiled a plan to put 5% of Anthropic’s shares into a fund that could be used to make donations to nonprofits or support its mission in other ways.

But details surrounding one important aspect of the artificial-intelligence company remain largely under wraps: the opaque trust empowered to shape its board and block major moves. Anthropic’s Long-Term Benefit Trust holds enormous sway over the company and is governed by documents that haven’t been divulged.

While investors run the show at most public companies and maximizing profits is the priority, Anthropic is set to be one of a few such companies established as a so-called public-benefit corporation—and even more unusually, steered by a trust.

The trust has no explicit vote in many shareholder matters, instead exercising power by appointing most of Anthropic’s board. It can seat four members of Anthropic’s seven-member board, and dismiss them without cause. Trustees can also block corporate actions. Its mandate is to steer AI for humanity’s long-term benefit.

Anthropic named the first five trustees. Now, the trust only has to consult the company when filling vacancies, of which there are two currently. Trustees include former Federal Reserve Chairman Ben Bernanke and chairman Neil Buddy Shah, head of the Clinton Health Access Initiative.

Anthropic has said the trustees are financially disinterested and unaffected by Anthropic’s material success. They own no Anthropic equity and don’t share in its profits, “compensated only for their time and service,” the company said online in July.

Trustees must consult with company leaders “on certain key matters,” Anthropic’s legal advisers wrote in 2023, without saying which. Anthropic must give trustees a five-day heads-up before issuing more than routine debt, selling half or more of the company, or transferring control of any AI model surpassing unspecified thresholds updated each quarter by Anthropic’s board.

Some legal experts say the notice requirement amounts to veto power, given the trust’s power to replace its board majority. An Anthropic spokeswoman said the notice requirement doesn’t give trustees veto powers, but declined to elaborate.

Other details are murkier, including when and how Anthropic shareholders might be able to override the trust.

Public-benefit corporations emerged over the last 15 years, in part to help boards guard against litigation where societal, environmental or other considerations in corporate decision-making clash with shareholder interests.

Delaware law says a PBC’s directors must balance the best interests of those “materially affected by the corporation’s conduct” with shareholders’ interests and its stated mission. In Anthropic’s case, that is to advance AI for humanity.

Seventeen PBCs traded publicly by 2024, University of Texas law professor Jens Dammann found, up from three in mid-2020. They include online eyewear retailer Warby Parker, with a roughly $3 billion market capitalization, and cloud-services company Veeva Systems, valued at around $50 billion. It is the trust that makes Anthropic stand out.

OpenAI, Anthropic’s chief rival that is also eyeing the public markets, is also structured as a PBC. But it is controlled by a Delaware charity, now called OpenAI Foundation, not a trust.

A public-benefit corporation’s mission can slip if the board loses focus, said Dammann, who has studied them.

“The directors are elected by the stockholders, and the stockholders benefit financially if the corporation strays from its mission eventually and focuses on profit maximization,” Dammann said.

Anthropic echoes this on its website, saying the trust will “hold Anthropic to its mission” and use its powers “to ensure that Anthropic responsibly balances the financial interests of stockholders with the interests of those affected by Anthropic’s conduct and our public benefit purpose.”Other such companies also have taken steps to insulate themselves from shareholders. SpaceX’s June IPO raised $86 billion with founder Elon Musk guaranteed near complete control. Alphabet and Meta Platforms also concentrate voting power in the hands of a few through multiple share classes.

Companies often revamp governance ahead of a stock listing. For Anthropic, substantial changes would still require navigating the trust’s broad power.

And without significant changes, “public shareholders will have very few governance rights,” said University of Colorado law professor Ann Lipton.

Investors might not care. The company is in the process of gauging investor appetite; The Wall Street Journal has previously reported it could raise as much as $100 billion in an offering that values it near $2 trillion.

According to a 2023 post on Anthropic’s website, shareholders can modify the trust and its powers without trustees’ consent if “sufficiently large supermajorities” agree. Anthropic hasn’t said how big the supermajority must be or whether it can act only in certain circumstances. The company’s most recent certificate of incorporation describes no such mechanism.

Under that document, eliminating or watering down the trust’s power requires its support, plus, in various cases, support from three quarters of the board or shareholder majorities as high as 85%.

Limits on the trust could be spelled out elsewhere, including in its own governing documents. But those aren’t public. Nor are agreements between the trust and Anthropic.

Write to Theo Francis at theo.francis@wsj.com