The deadline for a labor deal to save the season is less than a week away.
The sides met for the fourth day in a row at Roger Dean Stadium, the spring training home of the St. Louis Cards.
The union narrowed the number of young players who could earn additional major league service for accomplishments and loosened the restrictions on high amateur draft picks in consecutive years. Lower-revenue teams would be assisted by the latter.
They were going to have another day of talks Friday.
The players who remained from earlier in the week were the Yankees, Mets, and Cubs.
The players gathered in the first base parking lot before entering the ballpark.
Steinbrenner, Colorado Rockies CEO Dick Monfort and San Diego Padres vice chairman Ron Fowler were part of a management delegation that appeared to meet with the union for about 30 minutes before returning to the meeting room.
MLB made its stance public Wednesday, saying that it will cancel regular-season games if a contract is not agreed to by the end of Monday.
MLB said it will not agree to a method of making up missed games that the players have suggested.
If games are missed and salaries are lost, the union told MLB that clubs should not expect players to agree to management's proposals to expand the playoffs and allow advertisements on uniforms and helmets.
The sessions this week increased the total on core economic issues to just 10, as the baseball work stoppage entered its 85th day.
A minimum of four weeks of training is needed before the season starts. A deal would allow for a few days for players to report to camps in Arizona and Florida.
The size of a pool of money that would go to pre-arbitration players is one of the differences between players and teams.