Airport Extreme to 3 Sony Airplay speakers
Can you connect multiple Sony Speakers?  Yes.  Why wouldn't you be able to?

The AirPort Extreme is just like any other WiFi router in as much it is a router, a switch, and a WAP (Wireless Access Point) like any other wireless router.

The Sony speakers are just like any other WiFi speakers in as much they are clients on a WiFi network.

The real question here is does iOS support streaming to multiple AirPlay speakers simultaneously?

Currently, the answer is NO.  This is a limitation of iOS.

However, there is an App called Airfoil Satellite which gets your around this limitation.