No and No.
The memory allocated to the address book on the printer is limited to 50 entries (See page 179 of the CM2320 User Guide). For faxing its 120 entries. That is all you get. However, you can set up a service like HPs Digital Sending Service that can manage company wide address books for your printers if you have Active Directory. There is no limit to the phonebook size here since everything is saved on a remote server.
Multiple profiles is also not a possibility for any HP products that I am aware of. Its one address book to rule them all.