Pinnacle Phone and Data can supply and install corded and cordless Conference Phones.

Why do I need a Conference Phone, when my phone is Handsfree?
Handsfree phones are designed for personal handsfree use, in a regular sized room, with low ambient (background) noise.
Most handsfree phones only provide "one-way" talking, in other words, you talk, then you listen. If you talk while the other party is talking, your voice will over-ride their voice.
This is called half-duplex handsfree. The same method was used in the days of CB radio.
More recent (and usually, more expensive) handsfree phones use full-duplex handsfree, which enables continuous two-way conversation.

Conference Phones are designed for use in larger rooms (such as Board Rooms) with multiple participants, and also provide continuous two-way conversation.

There are a variety of types available from different manufacturers.

Polycom has many models for different needs, with both corded and cordless models.
Check out their website for more info.

    
Selection of Polycom Conference Phones

Panasonic produce a model that has a recording function to digitally record up to 120 minutes of conversation.

Panasonic Conference Phone