In lightroom desktop, Not classic, Not mobile How do I refine a search to add start ratings. After I am already have a filter

Hi! Yes, you can narrow it down the other way round too — star rating and person are just two criteria you can combine, in either order:

1. Open the Filter options (the filter icon) and set both: under Ratings, choose a star rating to show photos rated that high or higher, and under People, choose the person. The grid then shows only photos matching both.

2. Or use the Search bar with facets — Adobe's help lists both rating: and people: as search facets you can type in the Search bar, so you can add the rating there as well.

So after filtering by a person, just open the Filter options again and add the star rating — no need to start over from the rating.

More detail in Adobe's help (see "Search photos with facets" and "Filter photos"): https://helpx.adobe.com/lightroom/desktop/organize-photos/organize-photos.html