Yes, you can have a co-borrower on your loan. However, depending on the co-borrower, their relationship to you, and their status as a civilian or a veteran, it can affect your loan.
Spouses. When couples look for a home together, they often put both their names on the loan. Applying for a VA loan with your spouse as a co-borrower, regardless of their veteran status, is no different than with other loans.
Veterans. Except for a spouse, no civilians may co-borrow for a VA loan. Furthermore, the veteran you choose to be a co-borrower must intend to live on the property with you.
Whether they're your spouse or a close friend, purchasing a home with a co-borrower carries a degree of risk and must be thoroughly considered before any major decisions are made.