Thanks for adding the additional details. I think I understand your requirement.
It is not possible to add an extra object to the reference set selector. Nevertheless, it is possible to build this yourself. My suggestion would be to create a page with the context object you want to use. On the originating page, you can show a Datagrid (or another widget) in order to show the already connected objects. On this page, you can also add a Show Page button to your newly created page.
On this page, you can add a Datagrid with the selectable objects. The settings of the Datagrid should give you comparable options to the reference set selector you tried to use before. In addition to that, you can create your own Select button, in which you use a Microflow to attach the selected objects to the context object. In this way, you can show additional information while offering the same functionality as the reference set selector.
Hopefully, this is helpful. If it solves your problem, it would be great if you can mark this question as resolved. If not, please let us know.