The easy answer to this question is yes, pet mice can live alone. However, mice are usually very social animals, so there is a benefit to keeping them together. Although, if you want to keep multiple mice, you need to make sure they are compatible with each other. For example, you should never keep males together, as they will fight. Males and females together will breed incredibly quickly, and they can become territorial, even when they are from the same litter.
If you want to keep more than one, ensure they are female and have enough space for them all.