Shared voicemail boxes

We have tried all methods to enable this and do not have an option to share any of our calls. Currently, during business hours, we have a company greeting with options to go to one of 3 group boxes or they can dial extensions. We would like all team members to be able to access the voicemails for these group boxes but still have them routed so that specific people are first in line to answer them. Is this an option? Can we have shared voicemail for groups or only people? Can we have the company greeting route to these groups AND have shared voicemail?