No. The IRS sets the limits as individual for single policy holders or family for those covering themselves + 1 or more. So the family HSA that you have is all that can be set up for the 1 policy that you have.
DC is 19 y.o and is currently doing an internship where he expects to gross about 15K this summer. He will be contributing to a Roth. I was wondering if he can also contribute to an HSA if we did not claim him as a dependent on our joint tax return. He's currently on our family HDHP plan through my employer.