Could I house fancy mice with spiny mice?

you can't introduce male mice to other male mice at all. The only way male mice will ever get along with other males is if they were brothers born together and lived together their whole lives. Generally females can get to know eachother and get along, but it often depends on their tempraments. If some mice are aggressive, be it your original ones or the new, spiny ones don't try to make them all live together. Also, don't introduce a new mouse into a cage of females when one is pregnant or the baby mice haven't left the nest yet. I don't know about spiny mice (never heard of them, actually) but if they're known for aggression towards other mice be especially careful, and I wouldn't let them stay in the cage when you're not there like overnight until you're sure they're getting along.

When the baby mice are born and you separate the males from females you'll need a new cage for the males. They won't live with the older males. Even if one's their dad, they will not get along. At all.

Edit: Looked up spiny mice, and yeah. totally in love. But I don't think they can live with other mice. Seems they pick on smaller ones, especially if there's more than they're comfortable with. And the spiny's seem to like it pretty hot, which the other ones don't really like too much. But if you live somewhere warm anyway, that might not be too much of an issue. But, it looks like they do like mice, and are pretty sociable, but the issue is you need to avoid overcrowding. But for the life of me I can't find anywhere that talks about having spiny mice in with other mice.

I think you'll need 3 or 4 cages. one for the males you have now, one for the females and babies, one for the new baby male mice when you have to take them away from the females (you REALLY don't want to mess that one up) and one for the spiny mice if they don't get along with the other females.

As long as they are introduce properly and the same sex they're should be no issue at all