The 'double Dirac cone' 2D topological interface states found on the (001) faces of topological crystalline insulators such as Pb1−xSnxSe feature degeneracies located away from time reversal invariant momenta, and are a manifestation of both mirror symmetry protection and valley interactions. Similar shifted degeneracies in 1D interface states have been highlighted as a potential basis for a topological transistor, but realizing such a device will require a detailed understanding of the intervalley physics involved. In addition, the operation of this or similar devices outside of ultra-high vacuum will require encapsulation, and the consequences of this for the topological interface state must be understood. Here we address both topics for the case of 2D surface states using angle-resolved photoemission spectroscopy. We examine bulk Pb1−xSnxSe(001) crystals overgrown with PbSe, realizing trivial/topological heterostructures. We demonstrate that the valley interaction that splits the two Dirac cones at eachX is extremely sensitive to atomic-scale details of the surface, exhibiting non-monotonic changes as PbSe deposition proceeds. This includes an apparent total collapse of the splitting for sub-monolayer coverage, eliminating the Lifshitz transition. For a large overlayer thickness we observe quantized PbSe states, possibly reflecting a symmetry confinement mechanism at the buried topological interface.The recent experimental realization of three dimensional topological insulators has triggered an expansive program of research, driven largely by the accessibility and rich physics of the 2D electronic states hosted on their surfaces. 1-5 These states are often said to be protected, referencing two distinct concepts. Firstly, the electrical connection of a band-inverted and normal material is not possible without the existence of interface states that thread the bulk bandgap. Secondly, in many band-inverted materials some kind of symmetry exists that forbids hybridization between these cross-gap interface states, thereby ensuring that they remain metallic. These basic characteristics of topological interface states are dictated solely by considerations of symmetry and bulk bandstructure, and in the sense that these are not easily affected by perturbations at the surface, can be considered robust.However it does not follow that the interface states are immune to surface perturbations. For example, adsorption of non-magnetic impurities on the topological insulator Bi 2 Se 3 surface can dope the surface states. [6][7][8] Similarly, the topological crystalline insulator (TCI) Pb 1−x Sn x Se can be surface doped with Rb or Sn, 9,10 while lattice distortions that disrupt mirror symmetry open a bandgap. 11,12 For both classes of materials, the surface termination is predicted to play an important role in the topological band dispersions. [13][14][15][16] Details of the interface are also important in special cases where two bulk band inversions project to the same point in the surface Brillouin zone (Fig.1a), i.e...