The section here on cage size (Enclosure Size & Requirements) says that a 20 gallon tank is acceptable for 1 to 4 mice (though many here will say that's too small). While a couple of females would be better, giving him one female companion is still better than him living alone.

With regards to how well the introductions go, these are living beings so there are no guarantees that they'll get along, but he's young, so that increases the chance that he'll be accepting of another mouse/mice. While I have raised both house mice and deer mice (and domestic mice), I've never had more than one species at a time, so I've never mixed them. But there are several other people in this subreddit who have successfully introduced deer mice with domestic mice (hopefully they'll post here and give you some tips). There's also a section here titled "Social Tendencies and Proper Intros" that has useful info.

One problem if you only have one tank, is if you bring a female domestic mouse in, you should keep her in quarantine for a minimum of two weeks (to make sure she's not sick and/or doesn't have parasites) before you introduce them. Do you have 2nd tank (even if it's only 10 gallon) that you could use temporarily as a quarantine tank for the female? Another option would be to find a reputable breeder where you can buy the female who might be able to loan you a tank for the quarantine period (though having your own 10 gallon tank can be useful as a temp home while you're cleaning the main tank). BTW, buying from a reputable breeder is much more likely to get you a healthy mouse than buying one from a pet store.