How will reassigning tickets affect replies? If one client replies to the ticket and it gets reassigned to another client, do you show the other client's previous response to the new client?

Good question. I'm not sure what the right answer is, except that a ticket belonging to 1 client account, cannot be attached to replies belonging to another. My first inclination is to remove the relation and make the replies owned by the system. If a reply notice is added indicating that the ticket was moved from 1 client to another, it should be clear to the viewer why there are replies owned by system.

What do other ticket systems do?

I'm not sure what other system do in regards to moving a ticket between clients, but it may be easier for now to just allow assigning emailed-in tickets to a client since there is no "other client" to worry about in that case.

To start let's just allow an unassigned ticket to be assigned to a client. For example, client emails from a different address or opens the ticket in the form, then we can assign to their account as an admin.

I think re-assigning a ticket from an existing client to another client we can just reassign the client replies to the new client. On one hand we don't want to do that because we don't want to attribute replies to someone who didn't make them, so we should create a status or note like we do in other cases to indicate where in the thread the ticket was reassigned. The text in that can say something like:

"This ticket was re-assigned to [Client Name]. Previous client replies were re-assigned to this client and may have been made by another person."

So you want to move any tickets then? Contacts can reply to tickets too, so any replies by the client or any of his contacts would all be reassigned to the new client in the case you described.

Yes, any replies by the old client or contacts can be reassigned to the new client. Since we'll add a message within the ticket thread, it'll be clear which were converted... those previous to the reassignment.