Can multiple subsites use a single child theme?

I have a WPMU network where each subsite is the same -- except for colors, logo, and some content. I have been running about 20 subsites off of a single child theme (which makes it very easy to manage), but am now wondering is this is a bad idea.

Can I run multiple subsites off of a single child theme, or am I better off giving each subsite its own child theme?

Thanks,
Larry