Hi Paul.
Yes this is possible.
However, to do so it won’t be an easy task if you aren’t really familiar with coding.
You will have to add an event trigger when pressing the button in the repeater, it will have to save data to the user or to the task, and reload the repeater with the right data so it knows wich item it should show.
You would also need to filter evrything based on the memers label.
here are some links that might be usefull for your 
wix-Data
wix-Dataset
Repeaters
Kind regards,
Kristof.