We consider systems of backward stochastic differential equations with càdlàg upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces with a filtration satisfying merely the usual assumptions of right continuity and completeness. We assume that the pair $(H(U),U)$ satisfies a Mokobodzki--type condition. We prove the existence of a solution for integrable terminal conditions and integrable quasi--monotone generators. Applications to the optimal switching problem are given.