The Usual Suspects star and Spyridon Contogouris have already lost a legal battle with Costner over the sale of their shares in an oil filter device that could have made them multi-millionaires.
They claimed The Bodyguard star and his Ocean Therapy Solutions partners cheated them by hiding details about a deal made with BP following the Gulf Coast oil spill in 2010.
BP bosses made an $18 million (£11 million) advance payment for 32 devices developed by Costner's company in an effort to be better prepared for another oil leak disaster and Baldwin claimed he should have been told about the potential agreement before selling his shares in the company.
Baldwin lost the battle but now he's demanding a new trial because of excluded evidence, according to The Hollywood Reporter.
The actor and his partner have filed a $10 million (GBP6.25 million) lawsuit, alleging that Costner's attorney Daniel Grigsby demonstrated professional negligence and breached fiduciary duties by concealing details about the BP deal as he was drafting the buyout agreements for Baldwin and Contogouris.
Baldwin and Contogouris allege they were led to believe that there was no deal on the horizon, and therefore the buyout agreement that was drafted by Grigsby was a "sham".