Is it okay to take multi viatimins and zinc supplements at the same time, or is that just over-doing it?

It's OK as long as: Zinc has many benefits but you can have too much of anything. It depends on the dosage and form but generally it is considered safe to take 40 mg/day. The concern with higher doses is copper deficiency; if you take 1 mg of copper for each 15 mg of zinc it is safe to take more and higher doses are needed for some conditions. See http://ods.Od.Nih.Gov/factsheets/zinc-healthprofessional/.