Let $\mathcal X$ be a family of subsets of a finite set $E$.

A matroid $M$ on $E$ is said to be an $\mathcal X$-matroid if each set in $\mathcal X$ is a circuit in $M$.

We consider the problem of determining when there exists a unique maximal $\mathcal X$-matroid

in the weak order poset of all $\mathcal X$-matroids on $E$ (defined by putting $M_1\preceq M_2$ if every independent set in $M_1$ is independent in $M_2$).