So you want to run things like CUSTOMER1.YOURDOMAIN.COM and CUSTOMER2.YOURDOMAIN.COM ? And each subdomain will resolve to a different website, for each customer?
Sure. Easy.
Whoever runs your DNS NAmeserver (the servers listed in your domains WHOIS information, so this is usually your ISP), just have them make DNS A Records, one for each customer. So, your ISP would make an A record on their DNS server (that is your domains registered nameserver) for CUSTOMER1.YOURDOMAIN.COM resolving that to whatever public IP you assign to it, then make another DNS A Record for CUSTOMER2.YOURDOMAIN.COM pointing to another public IP address for that website.
Now, if all of these websites will only run on a single web server, and you are NOT getting separate public IP addresses for each customer website, then the different DNS A records could all point to the same IP address that your current www website points to, and you would just start rolling out Host Headers for each website, yours AND the customers' websites.
hope this helps