In order to run a second instance, or another web site for that matter, in apache you need to create a new configuration file in /etc/apache2/sites-available.
To run a second DSP, copy the current DSP’s apache config (dsp.local.conf) to a new file (like dsp2.local.conf). Edit that file and change the ServerName to the new instance’s domain name. Alias it as well if you like. Also, change the DocumentRoot and values to point to your second instance.
Secondly, check the original DSP config and make sure it’s set to your original domain, remain any unused aliases. And be sure to not alias DSP1 to DSP2 or vice versa.
The next step is to enable the new dsp:
$ sudo ap2ensite dsp2.local
And finally, restart apache:
$ sudo service apache2 restart
You can run as many DSP instances on a server as your hardware permits.
Let us know if you have any more issues.