Bob,
The functionality you are looking for needs to be supported the application. Generally speaking, most SSL application do. This allows an application to have different sites/users connect to it with different certificates.
Imagine if it didnt, there would be no accountability and tracking since everyone used the same certificate. If someone stole the certificates, you would have to re-issues new certs for all your users. If you used multiple certs, you would only need to re-issue new certs for those users/sites, that used the stolen certs.
The server sides keyring needs to contain the multiple sets of certificates used by the various sites/users.
When the client tries to connect to server for client authentication, it present it's certificates for validation. The server's keyring will be searched for the matching certificates. If found, the connection will be successful. If not found, the connection will fail.
Joe