Some will be ok in 2nd position and some will not and force you to refinance out the first - but those are options that are probably cheaper than credit cards 

Also credit score 680 with no missed payments over the last 2 years and also check their criminal report just to make sure you know who these tenants are, as the eviction process in New York city is very long and expensive. 

@Helena Goyvaerts rate for a 30-year fix would be at least 8.5% with some points (1% of loan amount).Most DSR lenders have a minimum credit score requirement from the applicant.

I was able to figure out that they had come upon some hard times and were significantly low on cash.

The Main St property in Grainfield, KS, offered a promising opportunity due to its low purchase price and strong potential for a high return after renovations.

There's a decent chance that if you have good credit and improve your DTI over the next year, you can put a Heloc on the property while it's still your primary to unlock some of that equity if needed.

Based on your numbers, and assuming you have a credit score high enough and have never filed for BK, you shouldn't have an issue getting approved for an HML to buy/rehab the property that I would estimate at about $370k-$375k (which includes 100% of the rehab costs).

But also with low debt or free and clear property that they can easily access any time in the future with a cash out refinance.

Was it included as a credit/debit on the HUD so it should have reduced your cash to close? 

I have a lot of colleagues with multis in Philly and all are doing well because of low taxes and high reliability, but it has its challenges.