Once again, thanks for your excellent and accurate description.
Here's an extract from the Bell System history:
CCSA -- Common Control Switching Arrangement
"Growth in public switching was paralleled by expansion of private line services, and, as might be expected, this required special services and featurs. In particular, arrangements were developed for No. 5 crossbar and No. 1 ESS so that the central office provided not only Centrex service for one or more customers but acted in nationwide two-level hierarchical private networks that served the telecommunication needs of large businesses. By dialing an access code, usually 8, the customer's employees could reach company or agency locations on the network. In order for the switching offices to be shared by several private networks, common-control switching was required, hence the name CCSA. A special 4-wire version of the No. 5 crossbar system was developed in 1960 to serve as the first or higher- level (tandem) in these networks."
"In many cases, CCSA networks include not only PBXs but also Centrex service from the same switching systems. CCSA service includes not only access to private network switching and transmission facilities, but also local and distant (foreign exchange) access to public network and dial or tie trunk facilities between PBXs connected to the network."