Instead of a reference selector, use a reference set selector - this will enable you to search for multiple records, select a number of them and assign all of these records to a user at once.
Alternatively, you could display a datagrid of the records, and create a small microflow to assign those records to the user. The microflow would receive a list of records (these would come from the datagrid) and also the user, and would then add the records received to the association between user and records.