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I think it is possible to set any phone up so that when somebody calls business1 you would see the phone number of the caller and the name of business1. and so on for each business.

the issue is with outgoing caller id. I am not aware of any phone being capable to switch between caller IDs. The only way to do that would be to change the outbound caller ID through the admin portal, which necessitates a reboot of the phone each time you want to use a different outbound caller ID.

The only way around the outbound caller ID issue is to use 5 different phones for each business. Or this could be 1 DECT phone with 5 different handsets. (still this would require that you have 5 licenses, in order to set up each handset with a unique outbound number)