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I'm Lucy, and I'd be happy to answer your questions today.
In order to terminate alimony, they have to be living together in a relationship similar to marriage. If he's only sleeping over half the time, that's usually not enough. They'd have to be spending the night in the same property most of the time, if not every night. The idea is that, when a couple lives together, they share expenses. If they're each maintaining separate residences, that's not enough unless you can establish that one of the residences is kept purely as a sham to keep receiving alimony.
Unfortunately, reduction is really an all-or-nothing thing unless her income changes. He'd have to be living there to get it reduced or ended. A person who spends 50% of their time in your house isn't necessarily contributing to 50% of the expenses - quite honestly, depending on if he contributes for food and stuff, he could be costing her more than if he weren't there. So, they have to be living together. I'm sorry.