Resolution
In order to set an alias for a specific domain you will need to do the following:
1. Enter the $HTTPD_VHOSTS_D/domain.tld/conf/
2. Create vhost.conf and vhost_ssl.conf files there and add the required alias records into them:
ServerAlias alias1.domain.tld
ServerAlias alias2.domain.tld
3. In order for the new files to take effect you should rebuild Apache configuration with the following command:
# $PRODUCT_ROOT_D/admin/sbin/websrvmng --reconfigure-vhost --vhost-name=<domain.tld>
Note: $PRODUCT_ROOT_D and $HTTPD_CONF_D paths are defined in /etc/psa/psa.conf
Note: since Plesk 8, domain alias for Web and Mail can be set in Plesk CP on "Domain->Domain Aliases" page. If the "Add Domain Alias" button is greyed out, the "Maximum number of domain aliases" limit should be increased for this domain.