  We define an operad in Top, called $\text{FM}_2^W$. The spaces in
$\text{FM}_2^W$ come with CW decompositions, such that the operad compositions
are cellular. In fact, each space in $\text{FM}_2^W$ is the realization of a
simplicial set. We expect, but do not prove here, that $\text{FM}_2^W$ is
isomorphic to the 2-dimensional Fulton-MacPherson operad $\text{FM}_2$. Our
construction is connected to the author's work on the symplectic
$(A_\infty,2)$-category, and suggests a strategy toward equipping the
symplectic cochain complex with the structure of a homotopy Batalin-Vilkoviskiy
algebra.
