Can a member of the church be re-baptized if they are excommunicated more than once?
It is possible. However possible should not be confused in any way with easy. When we are talking about ex-communication, the things that lead to them, and the path back, we are talking about things that are big deals.
In each case of someone wanting to be re-baptized it is evaluated based on the individual facts related to that case. Things like the details surrounding why they were ex-communicated in the first place and are they currently showing the signs of sincere repentance. As well as inspiration of the spirit.
In the case of a second go around they would once again evaluate everything. Naturally, depending on the details it could be very hard to seen as sincerely repentant given that the person is back after being thought to be sincere the first time. Therefore unless the situation was really abnormal (like an error on the part of the church) the first time around, a second time becomes increasingly more difficult.
Still ultimately they will be praying about it and seeking the Lord’s will on what action they should take.