I had rodent control remove them, place a cap on the chimney, and seal up a hole in the siding that they had used to enter the attic.

@Michael Mejia you nailed it with your last response. 

Jessica,Part of the preferred stock purchase agreement put a 7% cap on delivery of investment properties and second homes to Fannie and Freddie.

A bigger problem may be the cap on FHA loans if you're looking to purchase a 4plex in a high value area.

@Joshua Strickland and @Luke Carl nailed it on the head in my opinion. 

How much do certain mom and pops (nails, barbers, etc.) in similar properties pay?

On the refinance, with as little as 3 months of seasoning, you can get 80% LTV on a cash-out w/ a DSCR lender (30 yr fixed based on property cash-flow) -- there's no cap on the loan not exceeding your cost basis. 

My lease is fairly comprehensive and among other things, it explicitly prohibits nailing and drilling into ceiling joists in unfinished basements and garages.

Going by Mike's theory it makes more sense to put a cap on the total amount that can be sheltered that it does to limit the choice investment options.

And the issue you are having X years down the road is 1 nail pop?