If I provide two domain names for the same Server IP address can I get two different SSL certificates (one for each domain name)?

It is not possible to provide two domain names for the same Server IP address and get two different SSL certificates (one for each domain name).

It is however possible to get a Multi-Domain certificate, which is a single certificate containing more than one domain name, and that certificate is for a single server installation (most commonly used by hosting providers).

Also note that the use of Host Headers (which is how you can use a single IP for more than one SSL enabled domain) is not recommended for E-Commerce sites.

Dependent on the domain names a Wildcard SSL might meet the requirements, these are however more expensive due to the unlimited number of sub-domains they can cover. For example, a Wildcard for *.mydomain.com can be used to have SSL on any site where the * is replaced by a name, i.e., ‘secure.mydomain.com‘ or ‘gb.mydomain.com’, etc (there is no limit).