AirPort Extreme and AirPort Express Base

Sorry, not sure what you are asking.

Are you asking if the Airport Extreme can create a new wireless network and the AirPort Express be used to "extend" the AirPort Extreme network to provide more WiFi coverage?

Are you asking if the AirPort Extreme can "join" an existing wireless network provided by a 3rd party WiFi router using only a WiFi connection and "extend" the network that way?

Or, are you asking something else? If yes, please provide more details on exactly what the AirPort Extreme and Express will hopefully do. Please assume that we cannot see your network (we can't), so we will only know as much as you can tell us. In other words, things that might seem obvious to you are totally unknown to us.

The AirPort Extreme cannot connect to the network provided by your 3rd party router using only a WiFi connection.

The AirPort Extreme will need to be located a room or more away from your existing 3rd party main router.....AND.....it must connect back to the 3rd party router using a permanent wired Ethernet cable connection.

Then.....the AIrPort Extreme can be configured to "Create a wireless network" that uses the exact same wireless network name and password as your your "main" router and extend the network in that manner, since it will be broadcasting the same network as your main router.

Once the AirPort Extreme is set up and working, the AirPort Express can connect to the AirPort Extreme using a WiFi connection and further extend the network. Unfortunately though, this type of connection will result in a 50% or more loss of potential speed on the network, so the "AirPort" portion of your your network will be significantly slower than the "main" portion of your network.