I might not be seeing the correct option to do this, but it doesn't seem to be possible to filter the Browse list (https://itch.io/games) by more than one tag, unless you are just adding one of the "frequently used tags" that appear in the top list. In the latter case you can click the + to add that as an additional filter tag, but if you click the "View all tags" link to add a tag that's not listed, then any tag(s) you already had filtered by get removed.

This seems to be a bug unless I'm missing something. Clicking a tag in the "View all tags" list should add it to the list, not reset the list.