The house is still furnished and has one large throw rug.

I have a few single family properties that are rented out and I am looking to go into the larger multi unit property space (possibly a large apartment complex).

You have to be really careful in South Houston, it is a large area but most of it is areas most people would not invest. 

@Matthew Ward Any upgrading or remodeling would need to be capitalized and depreciated unless it's small enough to fall under the de minimis safe harbor rules but you'd need to talk to your CPA about that election.Generally a large part of remodeling costs would be considered tangible personal property that could be depreciated over 5, 7 or 15 years as opposed to the long life depreciation schedule of 27.5 years for residential rental property or 39 years for commercial property. 

I hope it's not a large amount!

Obviously, I have concerns about the margin of debt they have, especially since a large portion is unsecured debt.

Other than the AC, there is no other large expenses hanging over us.

To avoid moving my large family more than once, I want to know if there are any 2nd/jr lien lenders -OR - investor/venturers that would like to invest in the down payment requirement, in exchange for part equity ownership as a passive investment?

First, you can't take advantage of the economies of scale like you can in a bigger facility....meaning that as you expand, your revenue will increase faster than your expenses which will have a positive effect on profit. 

Other than partnering and syndication (exploring both), what financing strategies have you found successful in helping scale your rental business?