In this paper, we consider networks of N synaptically coupled excitatory-inhibitory neural modules, with N arbitrary. It has been argued that the connection strengths may slowly vary with respect to time and that they can actually be considered as inputs of the network. The problem that we are studying is which connection strengths should be modified (in other words, which connection strengths should be considered as inputs), in order to achieve flatness for the resulting control system. Flatness of the control network depends on the number of inputs and we show that if enough connection weights (at least N ) can be considered as inputs, then the control network is flat without structural conditions. If the number of inputs is smaller than N , then flatness imposes particular configurations of the interactions between the subnetworks (or even for the local interactions within a subnetwork). Our main contribution is to identify, analyze and characterize several flat configurations in the latter case.