This question already has an answer here:
If a family member dies without leaving any children to say Kaddish for them, can another family member take on the job of saying Kaddish? Is it permissible even if the parents of the one saying it are still alive?
I know that some people do not say the Mourner's Kaddish if both of their parents are alive. I am not certain if this is just a custom, or if it is actually forbidden to. If the parents do not object, then why would there be any problem with anyone Sanctifying the Name? Someone should say it for a Jew, right?