  We consider a non-relativistic (NR) limit of $(2+1)$-dimensional Maxwell
Chern-Simons (CS) gravity with gauge algebra [Maxwell] $\oplus \ u(1)\oplus
u(1)$. 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]
$\oplus\ u(1)$, which does not contain Extended Bargmann gravity (EBG); or, ii)
the NR limit of [Maxwell] $\oplus\ u(1)\oplus u(1)\oplus u(1)$, which is a
Maxwellian generalization of the EBG.
