Theranos Inc. plans to give additional shares to investors who pledge not to sue the battered blood-testing company or Elizabeth Holmes, its founder and chief executive, people familiar with the matter said.

The deal includes investors who participated in Theranos’s latest funding rounds, which ended in 2015 and brought in more than $600 million. Those investors could get about two additional shares for each share they bought, one of the people said.

The additional shares would come from Ms. Holmes’s personal stake in Theranos, some of the people said. That would result in her relinquishing her majority ownership of the closely held Palo Alto, Calif., company, some of the people said.

People familiar with the deal said it was approved by Theranos’s board in February. Investors are still reviewing terms of the proposed agreement, but most have signaled that they will sign off on it, these people said.

“This is an affirmative development for the company, providing a path forward in partnership with employees, investors and other stakeholders,” said Theranos director Daniel Warmenhoven. “Elizabeth elected to contribute her own equity to protect any dilution of shares held by other parties.”