The most robust solution is to individually toggle selected state on each item, and don't unselect all on a new click. Like a checkbox. Click once for selected

The most robust solution is to individually toggle selected state on each item, and don't unselect all on a new click. Like a checkbox. Click once for selected, once to unselect, don't unselect all on any click. A multi-select drop down is just solving the problem of a checkbox list being too long, or not what the designer wants it to look like. The most clear UI for this input type is a set of checkboxes in my opinion. Same for a single item select and radio buttons. Drop downs have a lot of caveats, and unique compositions in the wild, so many of them are inaccesible and it's essentially just because someone wanted it to look pretty. I think that is bad software.