I guess so - maybe the same as hamsters living alone. I think they are quite smelly though aren't they? With regard to lids, you can buy Zilla lids to fit most tank sizes on Amazon.com. Cage toppers would be good for a mouse too as they like to have something to climb I think (eg a branch).
https://www.amazon.com/Zilla-Reptile...+20%22+x+10%22
https://www.amazon.com/Ware-Manufact...pper+10+gallon
Sounds like one male mouse and your 10 gallon tank with a topper maybe, or a hamster and a different cage/tank.