FacetWP can be installed and used on separate sub-sites in a WordPress multi-site network setup.
However, FacetWP cannot filter or search across sub-sites, and there a no plans to support this in the future.
Note that each sub-site counts against your license’s site limit.
If you are using FacetWP with WordPress multi-site, it can be a hassle to have to add or change your facets and Listing Builder listings for each site individually, especially if you have many sites in the multi-site network.
Fortunately, there are two hooks available (facetwp_facets and facetwp_templates) with which you can register facets and listing templates programmatically. This way you can create and maintain your facets and listings in one place, your functions.php, as long as your network sites are using the same theme.
An added benefit of this approach is that your facet- and listing settings can be placed under version control, making it easy to revert to previous sets of facets/listings or previous facet/listing settings.