Well, typing Iodine LITERATE PRACTICIONER is one way to begin..
But the other way is to research the function of each nutrient, how they work in the body, and read the different threads folk have posted about each here on the CZ forums. Folk tend to collect the articles they find helpful, and repost them for prosterity's sake.
Aka, the search bar is your friend, wikipedia and nutritional sites, and especially threads here where folk tell about their experiences.
The classic companion nutrients are the minerals:
Magnesium, boron, potassium, selenium, salt (because of the chloride in the sodium chloride)
And the nutrients:
B2 (riboflavin), B3 (niacin, best inositol hexanicotinate form) vitamin C (ascorbic acid form)
You'll find that people start with those ingredients, and up or lower their intake according to how their body reacts. There's no set standardized way to do it because nutrients are a web of variables, not a set shape-
For example, some folk react really poorly to taking selenium because their methylation cycle is really keborkled. They need extra methionine to help process the selenium (of which tri-methyl-glycine is one of the miracle helpers there).
Boron's not listed on the stop the thyroid madness page, either, but CZ-goers love it for helping on the halide cleanup (pushing out the bromide and flourides which Iodine also helps displace).
No, you don't have to read everything by abraham, brownstein and flechas (I've only been able to read what I found links to on the Iodine VWT forum, and that was an article by abrahams about diabetes and iodine), but you gotta practice your google-fu to become wise in the ways of halide supplementation, grasshopper. ;)