CRM Cases created and managed via email reply on a tag  in the subject line to ensure the email goes to the correct case. When customers start a new email string that excludes the tag, a new case is created. There is currently no function to merge the two cases together.
Add a tab or field to the screen called Merge With that is a lookup of existing cases. Have an action or button to process which moves all content from the existing case to the Merge With case number specified.