Overlap is not allowed in Socreg. If two departments share a subnet, the department who claims the most IP addresses for that subnet will get the entire subnet. The other department will get individual IP addresses.
Additionally, one Security Contact will register and be primarily responsible for an IP address, although other Security Contacts may also receive security notices for that IP address.
For complicated situations, e.g., where two different groups are responsible for systems on a subnet, a Security Contact created just for that shared responsibility might be the best solution.