Is it safe to use a rinse over hair that is already colored with permanent color, and will it damage my hair if I do?

The real question is, "what is your definition of a 'rinse'". Many people consider a hair dye a "rinse".

If a rinse is something like Roux Fanci-Ful rinse then it's fine. You can use that as often as you like. Other truly temporary rinses (those that shampoo out with each shampoo) can also be used. If you wish to use a semi-permanent or demi-permanent, then we need to talk some more.