We propose a protocol for the construction and maintenance of multipoint connections (MCs). The protocol is based on link-state routing: information regarding multipoint connections is broadcast to network switches, which perform all computations locally. The protocol is generic in that it can be used with MCs of different types, including symmetric MCs, receiver-only MCs, and asymmetric MCs. Results of a simulation study show that this generality can be achieved with negligible (in normal traffic periods) to moderate (in very busy periods) signaling overhead.