A quaternary can mix 4 eluents (hence quat), and can be used when analyzing a complicated mixture, for a 3 component gradient, to include wash solvents or to just have 2 pairs of eluents (so you can pick and choose between 2 or more separations, without changing eluent bottles).
Instead of using four pumps, quats use one dual-piston reciprocating pump and a solenoid controlled portioning valve located in-line between the solvent degasser and the pump head.