Example: Chris is playing a deck with Brobnar, Mars, and Sanctum. Chris plays Hypnobeam to take control of a Saurian creature from Sam. On Sam's turn, Sam uses Snag to fight the Saurian creature, destroying it and forcing Chris to choose Saurian for their active house next turn. On Chris' turn, when they reach the Choose a House step, they are forced to choose a house that they cannot choose as it is not on their identity card and they don't control a card of that house. Since Cannot effects take precedence, Chris may freely choose their active house.