This article might be helpful. It breaks down each type of test, and what a positive results means in terms of the probability that you might have celiac disease. One test that always needs to be done is the IgA Levels/Deficiency Test (often called "Total IGA") because some people are naturally IGA deficient, and if this is the case, then certain blood tests for celiac disease might be false-negative, and other types of tests need to be done to make an accurate diagnosis. The article includes the "Mayo Clinic Protocol," which is the best overall protocol for results to be ~98% accurate.    

This article might be helpful. It breaks down each type of test, and what a positive results means in terms of the probability that you might have celiac disease.     

Multivitamins are generally not potent enough to effective address significant deficiencies.

Try a multivitamin maybe it will cover what you are deficient in.

Agreed, and I can't remember exactly and haven't got time to check, but I think my blood didn't normalise for eight years! For years I read this forum thinking why can't I get my numbers down - everyone else manages to.   But my gastroenterologist didn't seem to worry about it, which makes me think he either thought I wasn't complying to the diet, or he'd seen similar cases.