For a home equity loan, you generally need to leave at least a 10-15 percent cushion of equity remaining in the home. So if your home is currently valued at $300,000, you would need to maintain $30,000-$45,000 of equity after the loan. So if you still owed $200,000 on the mortgage, you may be able to borrow $55,000-$70,000 through a home equity loan. ($200,000 + $55,000 = $45,000 equity remaining, or 15 percent). Of course, this would depend on how much equity you've been able to build since buying the home.
The VA does not do home equity loans, but you can go through conventional lenders to get a home equity loan on top of a VA loan.