That seems contradictory. "Basic service" is something that would be offered on a "a la carte" basis, while a "family plan" is a bundled service that offers a discount. Generally speaking, when something is bundled, you cannot break it down into pieces.
I would guess that if you want your son to pay for his services, he would have to get his own independent account.
When I was young I had the choice of going onto my parent's account, or, getting my own account which would require an advance deposit since I had no credit history. I chose my own account, despite the deposit requirement, since I didn't want my parents to see my phone bill. They felt my toll charges were too high, but I felt it was my money and my college friends and dates. In this way I wrote out my own check completely independently from them. I recommend that method.