Are there any multi-handset cordless phones that allow you to talk on more than one handset a time?

There seem to be a lot of cell phone questions these days, so I just want to clarify that this is about old-school landline telephones (actually, I’m using VoIP, but whatever).

Anyway, we have one phone jack available, but we want to have phones in multiple rooms. We currently have a dual-handset cordless phone, but you can only use one handset at a time. If both my wife and I want to be talking to the person on the line, we need to resort to some stupid kluge solution (speakerphone, conferencing in one of our cell phones, etc).

The naive assumption would be that we could just turn on both handsets, and they’d both be engaged on the line they share. Apparently, that requires some fancier technology than our phone supports.

My question is: are there phones available that work like you’d expect them to? If so, anyone have a recommendation? What should I even look for? Is there a name for this “feature”?