Can a circuit with a GFCI be shared at the box?

Your question is a bit vague, but let's try a two part answer. If you have a GFCI breaker in an electric panel you should only have one connection at the breaker, but the breaker will protect all devices on the circuit.

If you are talking about a GFCI outlet, they are equipped to extend the GFCI protection to other non-GFCI outlets by using the proper "output" connection on the GFCI.