  Let $\mathbf{G}$ be a unipotent group scheme defined in terms of a nilpotent
Lie lattice over the ring $\mathcal{O}$ of integers of a number field. We
consider bivariate zeta functions of groups of the form
$\mathbf{G}(\mathcal{O})$ encoding, respectively, the numbers of isomorphism
classes of irreducible complex representations of finite dimensions and the
numbers of conjugacy classes of congruence quotients of the associated groups.
We show that the domains of convergence and meromorphic continuation of these
zeta functions of groups $\mathbf{G}(\mathcal{O})$ are independent of the
number field $\mathcal{O}$ considered, up to finitely many local factors.
