XXY teenagers sometimes grow very tall because they have insufficient oestrogen.
So even if your XXY son is taking testosterone, if it doesn’t increase at a steady rate like it does in XY boys, he may grow to be very tall anyway.
You might not know this but the testes convert some of the testosterone they produce directly themselves into oestrogen. Oestrogen is also produced in fat and in muscle, but the testes do the most converting.
If the testes are diseased they will not produce sufficient testosterone, there will be less conversion to oestrogen, and it is oestrogen that causes the long bones to stop growing. That is why females are generally shorter than males, they have more oestrogen earlier and their epiphyses (the ends of the bones, where they grow from) stop growing. Females have their growth spurt at the start of puberty and males at the end of puberty, for a very good reason.
It takes time for the testes to produce sufficient testosterone to be converted at sufficient rate to cause boys’ long bones to stop growing. XXY boys are then at risk of growing excessively tall because of a disease in their testes called Seminiferous Tubule Dysgenesis.
It may be appropriate to give XXY boys additional oestrogen as well as testosterone especially if they don’t have much fat or muscle?
Ask your sons’ doctor to think about this.