Checked out the link and noticed that it shows command line method. So what's with using command line with Plesk 11? Appears the page instructs how to setup a CentOS server with the Plesk repositories and if you have access enough to do that then one could also use epel, remi, and webtatic repos as well. All of those appear to have more recent versions of PHP and MySQL.
http://www.centos.org/docs/5/html/yum/sn-updating-your-system.html
while above says version 5 of CentOS, still applies to version 6 of CentOS.
Since you can use command line, would investigate installing git and do your installations (and after installed via git) upgrades to moodle via git. That would also enable you to upgrade from 2.4.3, to 2.5.x+, to 2.6.x and then upwards to 2.7 when ready.
Why march the site via the versions upwards? Well, while there are some that say one could hyperjump, what of things like the two assignment mods? Have you converted those to the new assign? There have been changes to quiz stuff as well. Marching upwards via git enables one to take care of those things with stable versions of Moodle (known to work and have been fixed/patched, etc..).
Since you have 2.4 currently, check out:
http://docs.moodle.org/24/en/Git_for_Administrators
Your first step then should be to get the current site running under 2.4 using git.
Once you've figured that out, it's easy to upgrade to 2.5.x. Pause ... check site ... backup ... then upwards again to 2.6.x. Pause ... check site ... backup ... then upwards again to 2.7.x when ready.
'spirit of sharing', Ken