SSL cert for public IBE portal

This is most likely a stupid question, but my knowledge of certificates is lacking!

I've installed an internally-signed SSL certificate on our FortiMail pair for internal clients connecting to FortiMail Webmail (for quarantine portal), and this works fine, certificate is accepted by browsers.

I've just began looking at testing IBE, with the Webmail page being publicly accessible for registration/message pickup, and I'm unsure how to apply a public SSL certificate for this connection which maintaining the internal certificate. I have a valid certificate and private key file uploaded already to the FortiMail for the URL, but I believe any clients connecting externally are seeing the internal domain CA signed cert, which is set as default.

Is it possible to have separate certs for the Webmail URL based on whether it is accessed internally or externally? Our internal and external domains are different.