Shareholders in Newton, Mass.-based CommonWealth can remove the board without cause if two-thirds of outstanding shares provide written consent, according to the hedge funds. Corvex Management LP and Related Fund Management LLC, which together own about 8.5% of CommonWealth's shares, in a statement said that the move is necessary to shake up a company that the funds believe has been poorly managed.

The funds have argued that a "misalignment of incentives" between the REIT and its external management team has been detrimental to the stock, and have been critical of director Barry Portnoy and his son, who is CEO of CommonWealth.

"Corvex and Related believe that their proposal to remove the entire board of trustees as a first step, if supported by shareholders, will send a clear and unequivocal message to Barry Portnoy and his son, Adam, that the time has come for them to be held accountable to the true owners of CommonWealth," the funds wrote.

The filing is the latest salvo in the battle between the funds and CommonWealth. Corvex and Related earlier this year came out against a CommonWealth common share offering and debt tender, offering to buy the owner of office buildings for at least $2.1 billion if it scraps the offering.

CommonWealth instead proceeded with the offering.

Corvex, which was founded by ex-Carl Icahn lieutenant Keith Meister, and Related said they have engaged with Deutsche Bank Securities Inc. as financial adviser. The funds in their statement said that Deutsche is highly confident of its ability to arrange third-party debt financing to replace CommonWealth's existing term loan and revolving credit agreement.

Shares of CommonWealth traded up 1%, to $22 apiece, in the premarket Wednesday.