Don't overdo it. There is evidence that overdose of vitamin D can have harmful effects. Sorry I don't have time to show studies but google it. Vitamins are not just harmless pills and I am wary.
That said, in places or seasons where there is a lack of sunshine vitamin D deficiency is common. Eggs are a natural source of vitamin D so now that there's less sun I give my boy an egg for breakfast several days a week.
To be 100% sure you can have his blood tested and see exactly how much more he needs. I personally would not just guess. I would do a lot of online research and use the more conservative estimates, or consult a doctor or nutritionist, at the very least.
IMO Americans can be careless about vitamins and take them as if they were nothing. I have become more and more cautious about vitamin use over the years and try to avoid too much regular use of extra vitamins. A whole foods diet is the best way to go for most normal healthy humans.