As has been clarified by a few people, the TPE cannot be "supplemented" by adding other players' salaries to a deal, the player you are acquiring has to fit the TPE. That means we can't use it to bring in one star if the salary exceeds the TPE value. I guess we could use the TPE to bring in a player at say $25M and then add a $10M player from the roster and trade the new player and the $10M player for a $35M player in a 3-way, although there always seems to be one more rule in the CBA that I am not aware of so I don't know this for sure.
The TPE can be broken up and used in multiple trades, I am pretty sure this is true. I think the more likely scenario is that it is used on two or three separate players in separate deals, all in the $10M or less range. I don't know who those players may end up being but that is enough to get a decent veteran wing off the bench for example. The TPE allows you to be opportunistic when the right player becomes available.