Yes, you can use Airport Extreme to do this, although the how is a little foggy.
What I know for sure:
First you have to configure your AEBS to be a remote base station under the WDS tab. You then specify the Airport ID of the base station that you would like to receive signal from (you can browse since remember Hex numbers can be a pain).
What is unclear:
I cannot find anything that says you must have two airport extreme base stations for this to work. Also I cannot find anything that says you must have two airport stations to get this to work (i.e. you could use 1 AEBS and 1 non-apple access point). In theory, you could just add the MAC address of any wireless device and have this work, but I have not attempted this.
If you decide to get the AEBS and try this out, let me know if it works.