If so, where could I go to apply and secure this type of loan?

@Christopher Winkler That's all good information to consider Chris but I don't necesarily think it applies to this specific scenario.

@Oren H. if you have equity in your primary home you can cash out, that rule only applies to investment property's.

Hello--I only own one rental property, but also live on the other side of the duplex, so those are my special circumstances that may not apply to you. 

This is entirely new to me.One other question, you mentioned this strategy can be applied to 4 units.

Pete,I know an excellent contractor, who if not up to speed to build would know who is,  Sean, with Applied Pressure in Norfolk VA.

This scenario applies primarily to a straight, traditional "cash" purchase. 

But, fall back a bit and talk with your bankers and tell them the exact situation and see if those funds can be allocated for that transaction - which is wishful thinking but worth the ask - but also search for and line up another deal where those funds can be applied. 

We are apply jointly and both make 60k+ a year just off of our day jobs.

(That should also apply to fix/flips, remodels, etc.)