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atlernatively you could put in a workflow or script to throw an error when they create one and the customer is blank

and to make sure I'm understanding this correctly, the custom center must mimic the Sales center. Right?

Yeah, it would be quite a bit of setup to do, including setting up new roles too

If someone wanted to, they could find a way to do it without doing it from the customer

Where as a scripted error after record load would be fairly bulletproof