The star claims Baxter Healthcare, which manufactures drug Heparin, is partly responsible for the hospital error, which left his children, Zoe and Thomas, fighting for their lives after they were administered 10,000 units of the medication, instead of 10.
In the documents Quaid alleges the twins' damage "may be permanent in nature" and is "likely to cause serious complications in the future".
He also claims the labels for Heparin are a "totally foreseeable and predictable" error and Baxter bosses should have taken steps to warn and to distinguish the drugs "knowing of the danger of an inadvertent mix-up".
Quaid is seeking medical expenses and punitive damages. He has also called on the healthcare company to create a fund to cover his twins' future medical expenses.
The actor and his wife Kimberly agreed to a $750,000 (GBP500,000) settlement with hospital bosses at Cedars-Sinai Medical Center in Los Angeles in 2008 over the near-fatal mishap.
Documents show the Quaids previously sued Baxter Healthcare over the drug's packaging, but that case was dismissed.