Existence of independent quasi-equational bases. II

If a certain condition holds for a quasivariety $\mathbf{K}$ then $\mathbf{K}$ contains continuum many subquasivarieties having a finitely partitionable $\omega$-independent quasi-equational basis relative to $\mathbf{K}$. This is true, in particular, for each almost $ff$-universal quasivariety $\mathbf{K}$.