  We consider constrained multi-Hamiltonian formulation for the extended
Chern-Simons theory with higher derivatives of arbitrary finite order. The
order $n$ extension of the theory admits $(n-1)$-parametric series of conserved
tensors. The $00$-component of any representative of the series can be chosen
as Hamiltonian. The theory admits a series of Hamiltonian formulations,
including the canonical Ostrogradski formulation. The Hamiltonian formulations
with different Hamiltonians are not connected by canonical transformations.
Also, we demonstrate the inclusion of stable interactions with charged scalar
field that preserves one specified Hamiltonian from the series.
