Unfortunally, no.
What I need is two independent meshes but they need to be compatible.
For example, on the first mesh I need a polynomial space over the partitioned edge, it would be something like a P0 over each pice, in total, 10 dofs
For the second square, P0 over the edges would give me 20 dofs
But the mesh inside, I can refine as much as I want, as long as the nodes for the edge partition matches the mesh in the volume