Quasivarieties of nilpotent groups of axiomatic rank $4$

We say that the axiomatic rank of a quasivariety $K$ is equal to $n$ if $K$ can be defined by a system of quasi-identities in $n$ variables and cannot be defined by any set of quasi-identities in fewer variables. If there is no such $n$, then $K$ has an infinite axiomatic rank. We prove that the set of quasivarieties of nilpotent torsion-free groups of class at most $2$ of axiomatic rank $4$ is continual.