A second grievance was filed by the union on the wide receiver's behalf Friday, according to multiple media reports, in an attempt to help Burress fight for the millions of dollars on his contract he could lose.
The first grievance, which was filed in December, challenged the suspension and fine given to Plaxico by the Giants after he accidentally shot himself in a nightclub in late November.
The union said that the team violated the collective bargaining agreement when it placed Burress on the reserve-non-football injury list, suspended him for the final four games of the regular season and fined him an additional week's salary for conduct detrimental to the team.
The 31-year-old Burress was booked and arraigned on charges of criminal possession of a weapon relating to the shooting in New York on Nov. 29.
He pleaded not guilty, posted $100,000 bail and left.
The shooting was the latest run-in that Burress has had with the team since signing as a free agent in 2005. He has admitted to being fined dozens of times for violating team rules. In addition to his suspension in September, he was also fined $45,000 by the league for abusing an official and throwing a ball into the stands in a game against the San Francisco 49ers on Oct. 19.
Burress was shot when he fumbled with the glass in his hand and the .40-caliber Glock that he was carrying in his pants slipped down his leg. The man who caught the go-ahead touchdown pass in the Super Bowl then reached for it and accidentally pulled the trigger and shot himself.
He faces a felony weapons possession charge that requires a mandatory minimum 3 years in prison.
The union filed another grievance on Burress' behalf earlier this year after the Giants suspended him for a game and fined him two weeks pay for missing a team meeting in September.
The two sides eventually agreed to cut the fine in half, saving Burress about one game's pay -- more than $200,000.
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