  Several explicit examples of multi-particle quasi exactly solvable `discrete'
quantum mechanical Hamiltonians are derived by deforming the well-known exactly
solvable multi-particle Hamiltonians, the Ruijsenaars-Schneider-van Diejen
systems. These are difference analogues of the quasi exactly solvable
multi-particle systems, the quantum Inozemtsev systems obtained by deforming
the well-known exactly solvable Calogero-Sutherland systems. They have a finite
number of exactly calculable eigenvalues and eigenfunctions. This paper is a
multi-particle extension of the recent paper by one of the authors on deriving
quasi exactly solvable difference equations of single degree of freedom.
