  Let $\Omega=(\omega_{j})_{j\in I}$ be a collection of pairwise non-isotopic
simple closed curves on the closed, orientable, genus $g$ surface $S_{g}$, such
that $\omega_{i}$ and $\omega_{j}$ intersect exactly once for $i\neq j$. It was
recently demonstrated by Malestein, Rivin, and Theran that the cardinality of
such a collection is no more than $2g+1$. In this paper, we show that for
$g\geq 3$, there exists at least two such collections with this maximum size up
to the action of the mapping class group, answering a question posed by
Malestein, Rivin and Theran.
