It is possible to override the templates used by loading them from the root directory of your theme (preferably a child theme) so you can customize the output to suit.
However, EE already includes the Event date in the default output for My Events so I’m not sure I follow what you are trying to do.
Can you post a screenshot showing the output you would like to achieve?
The support post ‘Change columns in [ESPRESSO_MY_EVENTS]’ is closed to new replies.
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Support forum for Event Espresso 3 and Event Espresso 4.