Tenant wants girlfriend removed from lease

[Dave Mills]

Good Evening All, 

I am in another sticky situation, my tenant wants girlfriend removed from the lease and this the second month of their year lease. 

They both call me and gave me insights of their situation, they both want to stay in the house, and here is what I got from the conversations.

Girlfriend(nurse) is making a lot more money and she wants to stay. 

Girlfriend says that boyfriend won't be able to make the monthly payments, but he wants her to leave. Last week he told her that he is leaving and this week he changed his mind and wanted to stay. It sounds like he is trying to force her hand, and Girlfriend asked me if there is anything I can do. 

Boyfriend wants to bring a roommate. 

I told them that they both signed the lease so they are both reliable. And also suggested that they can hash it out between each other and let me know who would be staying. So I guess, I can remove one of them from the lease, do I have a choice who can stay? 

Since I can raise the rent for at least another $300, Will it be better to cancel the whole contract and let them both go?