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Interface states in a 1-D photonic crystal heterostructure with multiple interfaces are examined. The heterostructure is a periodic network consisting of two different photonic crystals. In addition, the two crystals themselves are periodic, with one being made of alternating binary layers and the other being a quaternary crystal with a tunable layer. The second crystal can thus be smoothly transformed from one binary crystal to another. All individual photonic crystals in the superstructure have symmetric unit cells, as well as identical periods and optical path lengths. Therefore, as the tunable layer in the quaternary crystal expands, other layers will shrink. It is found that the behavior of the localized modes in the band gaps is dependent on whether there is an even or odd number of interfaces in the heterostructure. With certain sequences of all dielectric photonic crystals, topological states are shown to split in two, whereas for other heterostructures they are shown to vanish. Additional resonant Tamm states appear depending on how many crystals are in the heterostructure. If the tunable layer is frequency dependent, the band gap can still support topological/resonant modes with some band gaps even supporting two separate groups.