Over at ESPN, Keith Law walks through how Type A and Type B free agents are calculated and how they work.
The section that is of particular interest, to me anyway, is Law explaining something that I wasn't aware of (or, at least, if I was once aware of it, I'd since forgotten that I knew it).
According to Law, teams are limited to signing 1 Type A or Type B free agent if there are 14 or fewer such free agents in a given offseason, and can only sign 1 additional Type A or Type B free agent for every additional 24 Type A or Type B free agents in a given offseason, although they get a credit for any such free agents they lose.
It is kind of complicated, so if you have ESPN Insider (it is behind the pay barrier), I'd definitely encourage you to check it out for yourself...