Layered transition metal chalcogenides are promising hosts of electronic Weyl nodes and topological superconductivity. MoTe(2)is a striking example that harbors both noncentrosymmetric T(d)and centrosymmetric T phases, both of which have been identified as topologically nontrivial. Applied pressure tunes the structural transition separating these phases to zero temperature, stabilizing a mixed T-d-T matrix that entails a network of interfaces between the two nontrivial topological phases. Here, we show that this critical pressure range is characterized by distinct coherent quantum oscillations, indicating that the difference in topology between topologically nonvtrivial T(d)and T phases gives rise to an emergent electronic structure: a network of topological interfaces. A rare combination of topologically nontrivial electronic structures and locked-in transformation barriers leads to this counterintuitive situation, wherein quantum oscillations can be observed in a structurally inhomogeneous material. These results further open the possibility of stabilizing multiple topological phases coexisting with superconductivity.