Consider offloading an underperformer, or a high equity property and getting better, larger or more assets.

How do you think you'll get another 10% equity after 12 months of payments?

As an active-duty (soon transitioning) Air Force myself, I know the VA loan is a powerful asset for us.

If you put less than 5% down, your return on equity is likely sky-high.

Who is to say my dollar equals how many equity shares?

Depending on your current rate or if the current loan is short term or long term.

Our investment to value (ITV) in the notes we purchase is usually in the 50-60% range, a significant amount of equity to protect our position and our private capital position. 

Another thought - are you considering an FHA loan on the next one?

Get it under agreement for less than asking price and offer to bring the loan current and have them carry that loan.The way I see it is they are just getting MLS properties under agreement - the last five I looked at had been sitting on the market for more than 150 days (overpriced) because the payoff of the loan would not be satisfied at lower price point. 

If it is a credit/equity line, you could provide a lender letter that the funds are available immediately for funding - and cured any recission period.