Connecting a ticket to an account in CRM without changing the contact

Connecting a ticket to an account in CRM without changing the contact

I want to connect Desk tickets to accounts in CRM where the contact person on the ticket is not apart of that account in CRM. Right now the tickets with the same email address as in CRM are connected. 


Our customers sometimes hire agency's to implement our technology. When support tickets come in from an agency about the topics from that specific customer I want to change/modify the ticket a tiny bit to connect it to that CRM account for visibility. (without losing original contact). Can this be done with Custom fields? What are all of the standard connections between CRM and Desk? Can we trick it to be connected to an account in CRM without an email from the account.

We do not want to connect CRM to desk to sync contacts or accounts two way. Because we want to keep our CRM Contacts/Accounts clean.  but maybe a one way sync from crm to desk.

Got any Ideas, 
Thanks