Non-relativistic Maxwell Chern-Simons gravity

We consider a non-relativistic (NR) limit of $(2+1)$-dimensional Maxwell Chern-Simons (CS) gravity with gauge algebra [Maxwell] $\oplus u\left(1\right)\oplus u\left(1\right)$. We obtain a finite NR CS gravity with a degenerate invariant bilinear form. We find two ways out of this difficulty: to consider i) [Maxwell] $\oplus u\left(1\right)$, which does not contain Extended Bargmann gravity (EBG); or, ii) the NR limit of [Maxwell] $\oplus u\left(1\right)\oplus u\left(1\right)\oplus u\left(1\right)$, which is a Maxwellian generalization of the EBG.