I spoke with our Product Manager about your original question. Instead of deleting the AMCV, you would need to send the new CRM ID into setCustomerIDs() method in VisitorAPI. i.e. when the user clicks 'this is not me' set a new CRM ID.
Thanks for the clarification, I think I understand your use case now. I've done a bit of asking around and it seems you might have the ability to return segments based on a specific profile in AAM. Of course, you'd need to have access to AAM and I'm not very familiar with the processes. I'd suggest opening a ticket with the AAM support team and asking more about the profile merge rules.
This may end up being one of those use cases that is very hard, if not impossible, to accomplish since today's tracking is based on cookies and a set of users on the same browser are going to share those cookies.
I don't believe the Marketing Cloud ID Service has a method for requesting a new 'mid' value, as this would "cliff" that visitor in Analytics which is typically undesirable. The Marketing Cloud ID Service was designed to use the 'mid' value as the primary key for that visitor with Customer ID's as a secondary key. This way, you are able to give the same experience to a user across different devices/browser/sessions (assuming that user has been identified using a consistent customer ID via a login or other method on each device/browser/session)
Example: Device MID Customer ID Phone 123 ABC Tablet 345 ABC PC 645 ABC
Using Customer Attributes, you could then upload CRM data that indicates CustomerID ABC is a "VIP Member". Next, you could create an audience in the Marketing Cloud to be used in a Target campaign where all "VIP Members" got a special offer. Finally resulting in that same visitor receiving that same experience across all their devices.
Hopefully, this context helps you understand the way the ID Service was designed. As for your use case, how would a visitor be identified as customer ID "Customer_123" if they we'rent really that customer? It sounds as if your setting the Customer ID value before validating via login or another method.
If the AMCV was cleared, the next time the ID service runs it would return the same mid as before. Meaning, it would act similar to cross domain tracking. Have you tested clearing it in a testing environment? My thought is it won't fully clear unless both the demdex and amcv cookie was cleared. Are you using Customer ID's for each customer?