While this isn’t a natural dietary source of iodine, it is worth including on this list because there is a good chance you were already thinking it! It is indeed possible to get your iodine quotient from supplements, but as you might expect it is important that you practice caution as we know it is possible to consume too much of the mineral.
That said, you can go somewhat over and above the recommended DV without worrying about changes to your thyroid gland. The recommendation is that taking 0.5mg of iodine a daily or less should be safe and be unlikely to cause harm.
Consult with your doctor first though and make sure that you do not exceed that amount unless explicitly instructed to do so.