As mentioned, you need to talk personally with a lender while avoiding what was previously mentioned.
The simplest answer to your question, is that if you currently qualify for both mortgages, you should be able to get the second one. Unfortunately, there are a lot of other variabls that would come into play that you probably do not want to share openly.
If you can qualify for both the existing mortgage payment + a new mortgage payment then you could potentially purchase with VA first and then let your old home go into foreclosure. Some may not agree that is the right thing to do but I'm sure you didn't come here for a lecture on ethics.