If your kid is staying on your plan, he should probably decline the employer’s plan and save himself whatever premium they want him to pay.. This may, however, make him ineligible for other health care benefits they offer, like FSA. This differs from company to company.
If you have 2 plans, you run the risk of both expecting the other to pay and lots of confusion about who is primary and who is secondary and, ime, nobody paying in the meantime. It is unlikely, as noted upthread, that the secondary will pay what the primary did not – even if it’s not a lot as neither is designed as supplemental or gap insurance. But I suppose you could do both.