Tenant wants to get room mate due to rent increase

[Jack B.]

I am raising the rent by $200 a month while still renting $200 a month below market. Basically right now I'm GIVING away $400 a month. I split the difference with the tenant since she's been there a couple years and is now a single mom though she originally was with someone when moving in and now the lease is all on her only.

Anyways, she's a good enough tenant in that she doesn't bother me for trivial stuff. There were a few small stains on the carpet in one of the girls rooms and the living room last visit, but that's it. Otherwise they keep the place up. 

She realizes I'm still giving her one heck of a deal and wants to stay, however; she can only afford it if a room mate, someone she knows from work, moves in (with screening and all). I'm torn. On the one hand, it would be the least hassle solution. On the other, I could make ANOTHER $200 a month more by turning the place for full price, for a total of $400 increase. I've had a few bites at $500 more even....

The only reason I can think of to say no is the above, and the fact that it's not clear who's deposit to ding (assuming I charge the roomie a small deposit) if there is damage. While I have a ton of grad school stuff going on and stuff going on at work as well as 3 other rentals to manage and am short on time and would prefer she stay, I kind of assumed she would move on account of affordability and that I'd end up renting it at market price anyways, but either way, I'm still "winning".  Both give me more money, one gives me even more money but with some effort involved. I don't see too many issues with the roomie situation, but I figured I'd ask those who have horror stories about this...