On the first day eligible players could file for free agency, 20 took that step yesterday.
Elsewhere in baseball yesterday, four players filed for free agency to increase the total to 105.
Eligible players may file during a 15-day period beginning the day after the World Series.
Over all, 161 players filed this year, 2 more than the number who filed in 1986.
Alex Rodriguez and 32 other players filed for free agency yesterday.
Ten other players filed for free agency, increasing the total on the list to 80.
The first evidence that this day would be a little different came when the players filed into the team's practice facility earlier than usual.
Eight such players have filed, and the owners' labor relations committee has rejected them.
More than 210 players have filed for free agency, a record.
Last year eight players filed salaries of $1 million or more.