Is there a way to customize the existing editprofile.aspx page? like adding extra fields to the editprofile.aspx page in sharepoint Online?
You have to go to your SharePoint Online central admin, https://tenant-admin.sharepoint.com, and click on User Profiles in the left navigation. From there, you can click Manage User Properties and add any new properties that you want.
Edit based on your comment,
Possibly, but it would require some work to do, it would probably be better to make it a multivalue sting and bind it to a term store field.