  In this paper we complete the exploration of connected components of the
space of BPS Wilson loops in three-dimensional $\mathcal{N}=4$
Chern-Simons-matter theory on $S^3$. The algorithm is to start with a
supersymmetric Wilson loop, choose a preserved supercharge, and look for BPS
deformations built out of the matter fields in the proper representations.
Using this, we discover many new moduli spaces of nonconformal BPS Wilson loops
preserving a single or two supercharges, which are subsets of the symmetries of
the 1/4 and 3/8 BPS operators. Along with the those previously found in
arXiv:2012.07096, arXiv:2206.07390 and arXiv:2210.03758, the total moduli
spaces are closed under this formalism.
