Ken: I've fixed the More button (see the latest update of WikiTree BEE (v.30.1.6)). The results of that box (with the More button) come from the Relationship Finder page, which will show you a long list of most recent common ancestors between you and the other person if they exist. I'm showing only the first two. The 'More' button will (or should) show the rest of them.
The results are brought in the first time you visit a profile and stored in a database in your browser. After that, the previous results will be shown to you each time (so as not to kill the WikiTree server). If you think the results need to be updated as you've added more people or something, you can (at the moment) right-click the distance/degree number, which you should see on the connection finder button (one of the BEE buttons). (I should update this so that just clicking the box will refresh the results. (I've added this (these) feature(s) to the new, as yet unnamed, WikiTree extension, and in that, you can refresh it just by clicking the box.))
Oh... Glad you like it by the way. This is something I've always thought would be a good idea.