Throwing Shield Shenanigans

A player in my group is interested in making a offensive shield build. They found that if you get a quickdraw shield and modify it with the throwing shield property, that you can don it, and throw it all as a free action. Then, if they put it on a blink back belt, then it returns to their belt immediately after the attack is resolved.

Thankfully there is a rule that states you can only perform a reasonable number of free actions per turn… In this case… How many shield tosses would be a "reasonable" [mechanically balanced] amount?