A current constrained approach is proposed to calculate negative di?erential conductance in molecular nano-junctions. A four-site junction is considered where a steady-state current is forced by inserting only the two central sites within the circuit. The two lateral sites (representing e.g. dangling molecular groups) do not actively participate in transport, but exchange electrons with the two main sites. These auxiliary sites allow for a variable number of electrons within the junction, while, as required by the current constrained approach, the total number of electrons in the system is kept constant. We discuss the conditions for negative di?erential conductance in terms of cooperativity, variability of the number of electrons in the junction, and electron correlations.