Bayer shares tumbled as much as 5% on Thursday (May 27).
That after a U.S. judge threw out its bid to limit the cost of future class action lawsuits.
The cases concern allegations that its Roundup weedkiller causes cancer.
Bayer had offered to settle around 30,000 claims, in return for placing limits on the suits.
But that was rejected by the judge, who called the plan "unreasonable".
Now a lawyer for the German firm says it will ask the Supreme Court to quash defeats it suffered in jury trials.
Bayer points out that its product was deemed safe by the U.S. Environmental Protection Agency.
However, three cases have so far gone to trial, and in each one juries awarded tens of millions of dollars in damages.
About 125,000 people have alleged that Roundup caused their cancer.
Some 96,000 of those cases were resolved with a $9.6 billion dollar settlement.