Qualifying for 2nd mortgage while roommate stays at current home

[Josh Burtch]

Situation: I own a home with a friend. Both our names are on the mortgage. I'm looking at buying a place for myself. But with the current market in a bad place, and our mortgage rate of 2.75%, we both are hoping to hang on to the house.

My friend has offered to stay there and pay the full mortgage, and we would not make any changes to the title or mortgage. 

I've talked to a couple lenders, and they say that I would need 20% down to qualify for another mortgage that would only be in my name. 

Just wondering about the best way to do this, or other options for qualifying if anybody has been in a similar situation.