I'd have to know more to know how I'd adjudicate. A couple examples:
If Wizard A casts Dominate then Wizard B does the same, I'd have Wizard B's take precedence, as it's more recent.
If Wizard A casts Dominate then Wizard B casts Charm Person, I'd have the person regard wizard B as a friend, but Wizard A could still control them. If Wizard A directs them to attack Wizard B (and they are friendly because of the Charm spell), then I'd see it as being an action against their nature, granting a new save at +2.