  We introduce a novel harmonic superspace for $3d$ $\mathcal{N}=6$
superconformal field theories that is tailor made for the study of correlation
functions of BPS operators. We calculate a host of two- and three-point
functions in full generality and put strong constraints on the form of
four-point functions of some selected BPS multiplets. For the four-point
function of $\frac{1}{2}$-BPS operators we obtain the associated Ward
identities by imposing the absence of harmonic singularities. The latter imply
the existence of a solvable subsector in which the correlator becomes
topological. This mechanism can be explained by cohomological reduction with
respect to a special nilpotent supercharge.
