Your only solution now is finding where the rodent is getting in. Basement, roof, exteroir crack in brick- that's about it. Obviously, i'd check the roof last since it's going to be the biggest pain in the assn (unless the only time you hear the noise is when you're on the 3rd floor.) Your house is a rehab from a two family into a one, was there a fireplace at any point in your house? is there still a chimney? Do you have an attic or some kind of crawl space above your 3rd floor? I'll bet you do, as i don't recall your 3rd level being pitched the same as your roof.
Basements cause all sorts of problems, especially considering the area of the city you live in and the probably concrete block construction of your seller/basement. Is your basement like that basement we had on Waterman? if so, lots of ways to get into the interoir of your home that way. Get a flashlight and start looking. Better yet, send your wife down there first. lol.

One other place you might check...your dishwasher. Take off the bottom panel and look for mouse poop. That's where i caught the fucker in my last house, coming in through the broken seal around the waste pipe. I'll bet it's a mouse. If it really does sound larger than that, and i mean most definitely not a mouse, i'm betting it's a squirell, and you're got a hole along the roof line somewhere, or the chimney if you have one of those. Sucks man, you've got a really big house so it isn't going to be easy finding the source of the problem.
All the replies about living with the poor rodent, uh...no, kill that bastard any way possible. IF it ever gets past the interoir wall, your wife isn't going to appreciate it very much when she sees it scurry across the floor.
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