You need to first check the written rules for each airline as they are complex. After that you should call the airlines to confirm your understanding. A third bag is generally considered "excess baggage" and besides cost big bucks might not even fly on the same flight.
Years ago people said that a pakcanoe was within the size/weight limits common 20+ years ago, I have no idea if this still holds true, excess and overweight/size combo could cost you $300 per flight!