Why are you planning to add 3 multivitamins? The amounts shown in the multi's don't look like what we, typically, see; what's the percentage of daily value in each one? I find that taking the individual vitamins I need, works better than a multi. For instance, I take vitamin D - 2000 IU/day, selenium - 200 mcg/day, calcium - 600 mg X 2/day, B-12 - 1000 mcg X 1 injection/week, etc.
Taking vitamins isn't really going to skew your thyroid tests.