Large amplitude internal waves in a three-layer flow confined between two rigid walls will be examined in this talk. The mathematical model under consideration arises as a particular case of the multi-layer model proposed by Choi (2000) and is an extension of the two-layer MCC (Miyata-Choi-Camassa) model. The model can be derived without imposing any smallness assumption on the wave amplitudes and is well-suited to describe internal waves within a strongly nonlinear regime. Emphasis will be given to the study of solitary-wave solutions, shown to be governed by a Hamiltonian system with two degrees of freedom. Solutions with one-hump profiles exhibited for different asymptotic limits. However, the richness of the dynamical system readily becomes apparent when certain regimes relevant to real oceanic applications and laboratory experiments are considered. In particular, we reveal the existence of multi-hump solutions in the case when stratification is weak and the density transition layer is thin.