Create a flashback system.
Allow the narrator to suspend the current card state and instead give characters simply a wild strength and wild weakness card. Subplots or items can be given out by the narrator at the start of the scene. At the end of the scene, all cards in the flashback are removed and the card state is restored to what it was before the flashback.
This would allow for more non-linear storytelling and variation.
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Elfwreck commented
I love this - we definitely need more nonlinear story options. This would also work for dream sequences and certain AU/virtual reality stories.
I suppose the current workaround would be "create a new character, identical to your current one except for str/weak cards, and play that one for the flashback/dream/VR scene."