  Let $X$ be a product system over a quasi-lattice ordered groupoid $(G,P)$.
Under mild hypotheses, we associate to $X$ a $C^*$-algebra which is couniversal
for injective Nica covariant Toeplitz representations of $X$ which preserve the
gauge coaction. When $(G,P)$ is a quasi-lattice ordered group this couniversal
$C^*$-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by
Carlsen-Larsen-Sims-Vittadello, and under some mild amenability conditions with
that of Sims and Yeend. We prove related gauge invariant uniqueness theorems in
this general setup.
