I like the idea, but I think there'll be some problems with having the extra step start at the beginning of your next end step given that a lot of 'end of turn' stuff(such as temporary tokens disappearing, 'did you do X during your turn' effects triggering, etc.) triggers at that point in the turn. I'd make it work more like 'clocknapper' (which allows you to act during that step/phase as if it was your own), which should avoid issues like that.
But it is yours? It's happening on your turn and you are "take"ing it. I'm not totally sure. Paradox haze says gets. Maybe "At the beginning of your next end step, you get an extra step or phase of that type."
Also, messing with time is a perk. Like sundial of the infinite.
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