A quasivariety ℚ is Q-universal if, for any quasivariety \( \mathbb{V} \) of algebraic systems of a finite similarity type, the lattice L(\( \mathbb{V} \)) of all subquasivarieties of \( \mathbb{V} \) is isomorphic to a quotient lattice of a sublattice of the lattice L(ℚ) of all subquasivarieties of ℚ. We investigate Q-universality of finitely generated varieties of distributive double p-algebras. In an earlier paper, we proved that any finitely generated variety of distributive double p-algebras categorically universal modulo a group is also Q-universa1. Here we consider the remaining finitely generated varieties of distributive double p-algebras and state a problem whose solution would complete the description of all Q-universal finitely generated varieties of distributive double p-algebras.