From MLB.com's Barry M. Bloom:

The most commonly held misconception of this offseason is that the Yankees could have signed pitcher Ben Sheets or could still sign left-fielder Manny Ramirez if only there were a few million dollars remaining in the Steinbrenner bank.

Both assumptions are incorrect. According to the Basic Agreement, and confirmed by a top Major League Baseball official, once the Yankees signed CC Sabathia, A.J. Burnett and Mark Teixeira, they had signed their quota of Type A or Type B free agents under the collectively bargained rules established by management and the Players Association. ...

"If there were more than 62 this year, we should have agreed on an increased quota," Manfred said. "We did not. I think if [the Yankees] were contemplating signing another Type A player, they would've read the agreement and asked us what we wanted to do. They would've said they wanted to sign a fourth player and we would've had to do something with the union."

Mabfred went on to say that the Yankees have not asked.