Yes, you can get blood tests that check for levels of vitamins, hormones, etc. as well as iron. When the GP (or whoever it is) orders the blood test, they tick the boxes for what they want to know the levels of, so tell them in advance what you want monitored.
Although it probably depends on your GP surgery. At mine, you don’t ask for one - they give you one only if they think you need it/if they think there’s a problem.