Step-line recurrence relations for Meixner multiple orthogonal polynomials on interlacing lattices

We consider the product of two classical Meixner weight functions, whose arguments are shifted with respect to each other. Its reduction to the corresponding integer lattices generates a system of two discrete semi-classical weights. Under certain conditions, this system is perfect and has positive weights. Nonetheless, it is neither an Angelesco system, nor a Nikishin system.
The talk will be devoted to the four-term recurrence relations satisfied by the corresponding orthogonal polynomials. Passing to limits then gives coefficients of four-term recurrence relations for several other families of multiple orthogonal polynomials.