So for instance if you have two events on July 15 you only want the date on the left hand side to display once? If so, definitely possible – and you’d probably want to set up a template override for the following template:
pro/widgets/mini-calendar/single-event.php
(You can get a full description of how to set up and work with template overrides in our Themer’s Guide.)
In outline, you would probably use a variable to track the start date of the last event that was displayed and from there only display the date block if A) that variable had not yet been created or B) it was different from the date of the current event in the list.
I hope that gives you a few ideas – and good luck 🙂