"If there are from 39 to 62 [Type A and B] players [during a given offseason], no team can sign more than three." - Barry Bloom of MLB.com reports
However, C.C. Sabathia, A.J. Burnett, and Mark Teixeira are not the only type A or B players they have signed. By rule, any re-signed player does not count towards filling a teams' offseason quota. This is why we were able to bring back Andy Pettitte and Damaso Marte.
The only somewhat-big move you might see out of the Yanks is a trade of Nick Swisher or Xavier Nady. Like I've said though, I'd rather keep both.