Is there any way to have technicians restricted on the way they can change the group assigned to a ticket?

For instance, I have a ticket created with template X when the To email address is X@domain.com

I have support groups A, B, X and Y.

The template assigns the ticket to group X. 

I have configured the template's rules to remove groups A,B so the ticket can only be assigned to group Y.

So far so good. 

The problem is that, as far as I have been able to realize, this only works when the ticket is in the Edit/view mode, as the request view allows to change group and technician to any value available, which is all, A,B and Y.

Something like an implementation of a "Can assign tickets only to the following support groups" privilege...

Thank you!