bvtech,
That is a quality of an Intercom system not a phone system. Even the Mitel 3300 only has the capability to do that with one phone; I believe the feature was called Direct Voice or Direct Page or something like that.
Anyway, to get multiple people on a call together on the MiVO-250 system to communicate is called conferencing.
If you are only talking about one person answering then what you could do is setup a Hunt Group with the people you know they will want to call then have them call the Hunt Group and the first person to answer the call is talking to them.
Typically what happens is someone will perform a page and then the person being paged will call the person performing the page.
I think you need to work with the customer to understand what they truly want to accomplish as there are many ways to get people to talk to one another on any phone system, but you need to work within the limitations of the system you are installing and not by what you are removing.
Thanks,
TE