Hi Frédéric_VAUTHIER,
even that Plesk does not support major upgrades, you can still do them... mostly with only a few bugs to correct, so please take your time to investigate the issues, to be sure to find the real causes, to solve them.
... and "no"... you don't need a second server to do it - just make sure, that you backup your domains and databases and save them on your local hard drive untill you finished with the complete procedure and always keep the latest complete Plesk backup.
The reason why Plesk "does not support major upgrades" is the fact, that there are too many dependencies with all kind of basic software and Plesk can't guarantee a "smooth" dist-upgrade, because they don't code the operating systems itself. But Plesk gives as well a free migration support:
The "best" way to do major upgrades, is a step-by-step way. If you are on Ubuntu 10.04, please upgrade first to 11.04 and afterwards to 12.04. It can help to use "screen" (
https://help.ubuntu.com/community/Screen ) on dist-upgrades, because often enough you might get disconnected using ssh during a dist-upgrade.
It could help as well, to upgrade some software, before doing the dist-upgrades ( for example, upgrade MySQL, Apache2 and PHP to the versions, you would like to use with Ubuntu 12.04 ). You can investigate issues/problems much easier, if you delimit possible causes.
Don't panic when something went wrong - there are always some helpfull people here in the forums, if you experience issues/problems/failures and because Linux isn't Windows, there should be always ways to solve an issue. ^^