Is there a way to get a phone system that’s hosted elsewhere?

Our CFO wants to find out if there's an option out there where we can get a business phone system (but NOT VoIP) that's hosted somewhere else — similar to server hosting — and just have our phones and plug them in and go. The only thing I can think of like this is VoIP, but we are in a 2 year contract with Verizon for our 6 current phone lines, and he doesn't want VoIP. Is there anything out there that does this, or does he want something that doesn't exist?