The answers to questions like this are usually easy, as long as they are not our clients at the time; more money, less house, better credit.
How long has the SO been in the US? Depending on her status and the lender there may be some options to use her. There are some lenders who focus on immigrant loans. They sometimes pull credit from the home country; get letters from the US employer to verify job status and Visa status.
Another thought is that is he has debt which is limiting his DTI, can she pay some or all of it off? This would increase the buying power. If he has a car payment, and she needs credit she may be able to buy the car, put half down and get a lender to finance the balance building her credit and alleviating his debt.
It would be a win-win. He'd get a home instead of paying rent. You'll be able to help a great person and earn a good return on your money.