A one-dimensional discrete lattice of dimers is known to possess topologically protected edge states when interdimer coupling is stronger than intradimer coupling. Here, we address richer topological properties of photonic superlattices having an arbitrary number of elements in each unit cell. It is shown that the superlattice provides a tunable number of topologically protected edge and interface states depending on certain restrictions on intra- and intercell couplings maintaining inversion symmetry of the lattice. Simultaneous and stable propagation of multiple topological interface states, their interference pattern, and stable oscillation are reported. The configuration can be relevant for topologically protected mode-division multiplexing through a narrow route in photonic devices.