I discuss engineering strongly interacting phases of Majorana fermions on the surface of a topological insulator in contact with an s-wave superconductor. I claim that tuning a single parameter, surface chemical potential, one tunes between weakly- and strongly-interacting regimes. In particular, for the chemical potential tuned to the Dirac point of the surface the symmetry class BDI is realized. This setup opens possibilities to study a multitude of interacting Majorana models. In particular, I suggest 0d model to experimentally test the Fidkowski-Kitaev Z₈ periodicity, 1d and 2d exactly solvable models, 2d model analyzed by exact diagonalization, and one and higher-dimensional interaction-enabled phases.