Senior Star Management Co. said Thursday that it plans to offer owners of Five Star Quality Care common stock $3.45 per share in an effort to purchase up to 10 million shares, which would represent approximately 20% of outstanding shares. The move follows a $3-per-share offer that ABP Acquisition LLC made to shareholders Oct. 6 in a plan to buy the same number of shares.

In a statement, Senior Star urged shareholders of Newton, MA-based Five Star to take no action in response to the offer from ABP, a Newton, MA-based entity associated with Adam D. Portnoy and Five Star Managing Director Barry M. Portnoy. ABP also is affiliated with controlling shareholders of The RMR Group Inc. and its subsidiary, The RMR Group LLC, which is Five Star’s business manager.

Senior Star, headquartered in Tulsa, OK, said it has been monitoring events closely in the week since ABP made its offer.

“We are encouraged by the precedent set by Five Star’s independent board members in waiving certain ownership restrictions and granting certain approvals in order to clear the way for the Portnoys’ tender offer,” the company said. Senior Star said it expects to be granted similar exceptions and approvals by Five Star’s independent directors.

Senior Star founders William F. Thomas and Robert D. Thomas already own approximately 3.36 million shares of Five Star Quality Care, representing about 6.8% of outstanding shares. Senior Star provides independent living, assisted living, memory care, nursing care and home health services through its 2,200 units in 14 communities located in six states.

As of June 30, Five Star operated 276 senior living communities with a total of 31,191 units located in 32 states, including 214 communities (22,952 living units) that it owned or leased and 62 communities (8,239 living units) that it managed. These communities include independent living, assisted living and continuing care retirement communities as well as skilled nursing facilities.

“Senior Star’s interests are truly aligned with the interests of all shareholders in providing fair value for any shareholders who may be seeking liquidity for their investment on the one hand, while continuing to seek to take steps to improve the company’s corporate governance and strategic direction to drive shareholder value creation for long-term holders on the other hand,” Senior Star’s statement said.

The Thomases made a $325 million bid for 33 Five Star properties in December 2015, but Five Star rejected it.

Selling owned assets was one part of a “profound shift in strategy” that the two men recommended in a seven-page letter to Five Star in March. Other parts of the needed strategy, the Thomases said, involved investing in existing leased communities, employing lease de-leveraging and expanding the existing unit base.

The day after receiving the letter, Five Star President and CEO Bruce Mackey told those listening to an earnings call that the interests of the company’s board members aligned with those of shareholders. Five Star’s board, he said, was focused on improving operations and earnings through expansions and acquisitions, although he added that the company planned to sell some communities and convert some skilled nursing beds in continuing care retirement communities to private suites for rehabilitation.

Five Star sold seven of its 33 senior living communities to Senior Housing Properties Trust in June, but the Thomases said the company remained undervalued.