Importing an External ID to use when creating an Email to Case?

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We are implementing Email to Case.  In our organization, cases are opened under accounts, NOT contacts.

We would like to send an external ID as part of the email that opens the case.  This ID (which ties to a unique External ID field under each account) needs to identify the account in Salesforce and open the case in its name (rather than using the email address to tie to a contact -- this isn't helpful to us, since we don't open cases under contacts). 

Any suggestions?  Everything I read shows email to case as opening cases based on an email tying to a contact.  Thank you!