This year, a few groups of people have proved that certain Legendrian links in R^3 have infinitely many exact Lagrangian fillings that are distinct under Hamiltonian isotopy. The common approach of these groups (Casals-Gao, Gao-Shen-Wang, Casals-Zaslow) is through microlocal sheaf theory and clusters. I’ll describe a different, Floer-theoretic approach to the same sort of result, using integer-valued augmentations of Legendrian contact homology, and I’ll discuss some examples that are amenable to the Floer approach but not (yet?) the sheaf approach. This is joint work in progress with Roger Casals.