Quote from @Jeffrey Hill:
There are a couple of challenges with financing the difference. 1) The current servicer has to approve it. 2) Finding a lender to do a 2nd mortgage at 100% CLTV is almost impossible. You might find a local credit union or community bank that will go to 95 -100%.
At one point I called 2 different VA Regional Loan Centers regarding this section in the VA lenders handbook:
Assumability - The second mortgage should not restrict the
Veteran’s ability to sell the property any more than
the VA first mortgage. That is, it should be
assumable by creditworthy purchaser(s).No surprise, I received different responses from the RLCs. One said the 2nd mortgage has to be assumable and the other said it did not.
VA issued Circular #262417 back in August to try and clear up the issue:
Assumability: If the secondary borrowing is not assumable, the holder of the VA guaranteed loan should counsel the assumer that this may restrict their ability to sell the property to another creditworthy assumer through an assumption in the future.The lender currently servicing the loan still can decide whether or not they'll allow the 2nd.
You could do seller financing for the gap and then refinance just that amount with a Home Equity Loan or Line of Credit at some point down the road.