NEW YORK (CNN/Money) - Vioxx testimony could finish up this week in a New Jersey courtroom, but another group of plaintiffs' lawyers are teaming up to take on Merck & Co. in state courts, according to a news report.

The group claims to represent about 20,000 Vioxx cases and is expected to file court papers Monday telling Merck (up $0.05 to $26.23, Research) and the judge overseeing the federal cases that these plaintiffs only aim to fight the company in state courts and want no part of the federal litigation set to start in November, the Wall Street Journal reported on Monday.

While Merck prefers to battle in federal court, the group of lawyers want to try more cases faster in order to keep Merck scrambling and possibly to collect more fees, the Journal reported.

Merck, the New Jersey-based drug giant, pulled its painkiller Vioxx from the market in September, 2004 after a test linked the drug to heart attacks and strokes in some patients who took it for more than 18 months. Since then, more than 5,000 suits have been filed against the company in federal and state courts by former Vioxx patients and, in cases of wrongful death, by their family members. Judge Eldon Fallon of federal court in New Orleans is overseeing the cases that are consolidated in multi-district litigation. Following the destruction by Hurricane Katrina, federal litigation was moved to Houston.

Merck's lawyers have consistently denied that Vioxx caused anyone's heart attacks and dismissed accusations that the company tried to cover up negative information about its blockbuster arthritis drug.

"Merck continues to be committed to defending each of these cases on the merits," said Bruce Kuhlik, Merck's associate general counsel, according to the Journal. "We have the resources and the resolve to defend the company in these cases, wherever they may be, over the course of many years."

The third Merck trial was originally scheduled to begin Monday in Edinburgh, Texas, but plaintiff lawyer Mark Lanier told CNN/Money that the trial is postponed, possibly as late as April.

Lanier won the first trial on behalf of plaintiff Carol Ernst, successfully suing the company for $253 million in Angleton, Texas. However, state laws will prevent Ernst from collecting that full amount. To read more about the first verdict in the Merck trial, click here.