Application for iPhones - how to do it?

Does anyone know of a product whereby you can put your iPhone into a base station and then have it connect to multiple phones within your house, such that you can pick up an incoming call or make outgoing calls from multiple phones in several rooms of your home? Of course you can do that today with conventional phones, but I have never seen it done with a cellular.

Yes. Very simple and available on specific models of cordless phones from multiple companies.

Look for a cordless phone set that says something like Link-to-cell (Panasonic) or Bluetooth.

Vtech models with Bluetooth support pairing up to two cell phones as well as being connected to your landline if you have one (not required). You can even set the ring tones to be different for different 'lines'.

Once your phone is paired to the base, all handsets will ring throughout the house and you can make outbound calls from any of the handsets as well.

There's no physical connection between your cell phone and the cordless base and you do not need any apps. But your phone must be within 20-30 feet of the base since that is the practical range of Bluetooth.