Hello,
Yes, it is possible. the system is called as shared hosting. While adding the IP to your machine or server you need to add the IP as shared IP (which is default in case of cpanel and in case if your are using plesk you have to select the options while adding the IPS...). Once you have done that you need to register the name servers for the machine using two dedicated IPS and set the same in the server. Once that is done what ever domain you will be hosting in this server should be provided with the the name servers that you have set in the server. After the domain is set at registrar's end, then you can set the domain at your end or the server end. Make all the respective entries in the particular conf files and the see that you have db files or the dns entries created in the dns zone of the server.
Thank you.
Regards,