The inventory of types of office phone systems has evolved over the last several years. There are a few well developed options to consider.
The regular phone system technology is still very much alive. They call it POTS (Plain Old Telephone System). You can buy multi-line telephones that use the same analog transmission as was invented by Alexander Graham Bell. You can still purchase individual phones and telephone lines for each of your offices and pay the phone company a bulk rate for line services.
You can purchase multi-line systems that may route several lines through a single switching device that connects