Perturbation theory is developed for interaction of strongly nonlinear solitary waves close to the limiting, tabletop solitons (Π-solitons). The method is based on representing each soliton as a compound of two kinks so that the interaction of N solitons is treated as the interaction of 2N kinks. As an example the Miyata–Choi–Camassa equations for a two-layer fluid is considered. Equations for kink coordinates are obtained and analyzed. Some nontrivial features of two-soliton interaction characteristic of the strongly nonlinear case are established.