The site awareness feature uses volume tags, and the enforcement is done on the mirrors of a given volume. The limit on the number of mirrors of a given volume is 32, so that's the limit.
Now, if you're not really using the site awareness feature, and are just using the site tag name for tracking or inventory or reporting, then your constraint is how many tag names you can stuff into the private region --- but for that use case, you're probably better off creating your own volume tag rather than using the predefined site tag.