Can a team with cap room sign all the free agents it wants (up to the salary cap) and THEN re-sign its own free agents using the Bird exception?
A team’s ability to do this is very limited. The team’s free agents continue to count against their team salary (against the salary cap). This charge is called the “free agent amount.” There may not be enough money available under the cap to sign another team’s free agent, because the team’s own free agents are taking up all their cap room.