It's a complex topic which takes time to learn.Another metric you're going to need to look at is Debt Service Coverage Ratio, DSCR.

Look at DSCR loans (debt service coverage ratio) loans as another possibility.

DSCR loans are asset based (DSCR = debt service coverage ratio) and have refinance options up to 75% of current value.

Most places I quoted were around the same cost though the liability coverage varied.

The less obvious coverage I see often, is ACV over RC.

In NY, due-diligence title search has county and municipal searches which includes open permits, CoO and any outstanding county tax liens I think if you read the Conditions section of a title policy you'll find coverage is only for matters recorded in the public records which is probably defined in the Definition section of the policy as those records intended to impart construction knowledge to third parties. 

There are some great replies in here already but I would also want to suggest the use of virtual management software as a supplement to traditional management as well.There are some powerful software tools out there that essential manage all of those units from your computer screen (collect rent, process maintenance tickets).Hire a local handyman and they can act as your boots on the ground in case of notices or emergencies.This may help you save a couple hundred bucks down the road from the rising prices that management companies are charging now. 

@Derrick Wortman   Debt service coverage ratio is the right product for you.

Replacement Cost coverage (RC) for building vs Actual Cash Value (depreciated).  

If your insurance coverage isn't enough, they could seize the LLC assets, but not your personal assets.Additional thoughts:1.