Is it possible to update the Ubuntu software center in maverick to 4.0 ?
I have tried adding
deb http://us.archive.ubuntu.com/ubuntu/ natty main to software sources but installation failed (lot's of version problems)
You will not be able to update Software Center via the official repositories.
I don't believe that you will be able to use version 4 of the Software Center in maverick. It hasnt been backported.
The software store developers produce a daily build - as the name suggests, its not tested, but contains the latest changes on a day-to-day basis. However, I dont see any evidence that that has built successfully for sometime.
I would contact the software-center developers themselves (file a bug report via that link) if there was any intention to have version 4 available for maverick. Its probable that it is just a recipe build packaging mistake by the maintainer Michael Vogt.
PPA with USC daily builds -- https://launchpad.net/~software-store-developers/+archive/daily-build
Actual version for Maverick is 4.1.20~bzr2217