I remember my mom was a big believer in supplements and started me on them early on. Don't recall exactly what she was giving me, but I do remember learning to swallow multiple tabs in one gulp.
Don't believe anything I gulped down causing any trouble, but I worry she did get a bit carried away.
Giving supplements to children is a touchy subject, as "informed consent" is replaced with parental judgement. I would tend to err on the side of a very conservative protocol of a basic LOW DOSE multi. Children and young adults seem to do quite well despite the atrocious diets they often consume, so overkill with multiple boutique supplements would appear to be unnecessary and unwise.
As "eating one's vegetables" is often a major problem with children, flavonoids and polyphenols would seem to be a primary area of concern. Fresh fruit might help, or perhaps a small amount of weak green tea might provide both flavonoids and polyphenols. This would be what I would be worried about with children living on carb/protein dominant diet. Eggs also have been called natures perfect food, and may provide quality protein, choline and vitamins the child might not be getting elsewhere.