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Hamadène and Jeanblanc provided a BSDE representation for the resolution of bi-dimensional continuous time optimal switching problems. For example, an energy producer faces the possibility to switch on or off a power plant depending on the current price of electricity and corresponding comodity. A BSDE representation via multidimensional reflected BSDEs for this type of problems in dimension larger than 2 has been derived by Hu and Tang as well as Hamadène and Zhang [2]. Keeping the same example in mind, one can imagine that the energy producer can use different electricity modes of production, and switch between them depending on the commodity prices. We propose here an alternative BSDE representation via the addition of constraints and artificial jumps. This allows in particular to reinterpret the solution of multidimensional reflected BSDEs in terms of one-dimensional constrained BSDEs with jumps. We provide and study numerical schemes for the approximation of these two type of BSDEs