  We present a consistent BPS framework for a generalized
Maxwell-Chern-Simons-Higgs model. The overall model, including its self-dual
potential, depends on three different functions, h(|{\phi}|,N), w(|{\phi}|) and
G(|{\phi}|), which are functions of the scalar fields only. The BPS energy is
proportional to the magnetic flux when w(|{\phi}|) and G(|{\phi}|) are related
to each other by a differential constraint. We present an explicit non-standard
model and its topologically non-trivial static configurations, which are
described by the usual radially symmetric profile. Finally, we note that the
non-standard results behave in a similar way as their standard counterparts, as
expected, reinforcing the consistence of the overall construction.
