Three general classes I see:
1. Possession counters. You may force other players to do bad thing X, you MUST force other players to bad thing X. Chips and attacks both work well here. E.g When you play this card you may give each other player a curse. When you play this card you MUST give each other player a curse.
2. Masq/ambassador fun. When this card is first gained, the you may gain 3 VP chips. When this card is gained a second time, you may give the first owner 5 VP chips from the supply. Changing both of those to musts, makes this a much more powerful card in a few circumstances without weakening it all.
3. Swindle juice. When you gain this card you may give the current player 2VP chips. When you gain this card, you must give the current player 2 VP chips.
The biggee I'm seeing is that there are some circumstances where you want to buy this for yourself and you want your opponent to have make a decision with your card. Masq, swindler, ambassador, and possession all allow you to get a card of your choice into your opponent's decision space so it should be easy to write up situations where cards that interact with these are better as "must" than "may".