Party level ups

Howdy - I’ve been playing for a few years and have tasks that are still not done because I can’t level up my party’s.   I just opened 20 packets...and not one piece was one I didn’t already have.   

is there a strategy for leveling up a specific party?  Playing the party you want to level up doesn’t seem to increase your likelihood of a pice for that party.   Why not just play the same party all the time, right?  Doesn’t seem to matter what piece you get (which is very far and few between for advancement).