Stable interactions between higher derivative extended Chern-Simons and charged scalar field

We consider inclusion of interactions between the higher derivative extended Chern-Simons and charged scalar field. We demonstrate that the order N extended Chern-Simons and order 2n charged scalar admit the (N + n)-parameter series of interaction vertices. The interactions are in general non-Lagrangian, but they preserve a certain conserved second-rank tensor, whose parameters are determined by the coupling. The 00-component of this tensor can be bounded even if the canonical energy of the model is unbounded before the inclusion of interaction. If the 00-component of conserved tensor is bounded, the theory is stable.