Possible to group by referenced entity field?

Is there a way to group events by a referenced entity field on the view? I've got different exam rooms (referenced entities) that all need to be displayed on the same one page.

I've put together a view that that renders the different views for each exam room in a grid, but the issue I'm having is that they all have their own individual pagers. I would like them to all share a pager, so that there is one overall link to change the day or change from day to week view.

I've tried both Views Table Group and Calendar. They provide something similar to what I need, but I also need the drag and drop functionality from fullcalendar. Also, other issues arise from using them over fullcalendar, such as no overlapping of time fields in table and the exam room column only shows if there is already an appointment in it.

is this possible with full calendar?

I've attached two images: pic1.png is what I have done, pic2.png is what the client has requested.