  In this paper, we study a system of second order integro-partial differential
equations with interconnected obstacles with non-local terms, related to an
optimal switching problem with the jump-diffusion model. Getting rid of the
monotonicity condition on the generators with respect to the jump component, we
construct a continuous viscosity solution which is unique in the class of
functions with polynomial growth. In our study, the main tool is the notion of
reflected backward stochastic differential equations with jumps with
interconnected obstacles for which we show the existence of a solution.
