Check 1:
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Hard to tell why "none" works for some servers and doesn't for others - perhaps that may depend on PHP version installed. The following can be suggested to you:
1) set open_basedir to "{WEBSPACEROOT}:/tmp/" - while it doesn't make open_basedir comletely disabled, this setting will make your site able to include files from any other folder in your space, which should be enough for most cases
2) upgrade to Plesk 11 at http://parallels.com/download/plesk/11 - it is in pre-release phase and includes pre-configured "none" option for open_basedir (simply choose in dropdown menu). This one would completely disable open_basedir for your site
Check 2:
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To modify this setting, create a vhost.conf file in your /var/www/vhosts/domain.com/conf/ directory, and enter the following lines:
<Directory /var/www/vhosts/domain.com/httpdocs>
php_admin_value open_basedir /path/you/require:/another/path/you/require
</Directory>
Then
/usr/local/psa/admin/sbin/httpdmng --reconfigure-all
