When I visit a website that requires PKI client certificates Firefox will allow the user to select which certificate to present.
How do you present a different PKI client certificate to a server once you have already presented one, in Firefox?
This blogpost describes what you are looking for:
To clear your SSL session state in Firefox choose History -> Clear Recent History... and then select "Active Logins" and click "Clear Now". Then the next time you connect to your SSL server Firefox will prompt for which certificate to use.