The existence of topological interface states is investigated at the boundary between a binary photonic crystal and a quaternary photonic crystal, with each possessing inversion symmetric unit cells. Conditions are established that describe where the quaternary crystal can exist in parameter space subject to constraints. The closing of band gaps is discussed for different optical path ratios. When the binary and quaternary crystals share an interface, optical states appear at the interface when the two crystals have different signs for the surface impedance. The evolution of the states is displayed as the geometry of the quaternary crystal changes.