Is it possible to create a webserver that will serve multiple HTTPS domains on a single public IP address? I know HTTP will support this, but what about SSL/TLS?
I am not interested in wildcard certificates such as *.example.com, because I also need to serve websites for *.example.net.
You can do it through SNI and SAN/UC. SNI takes some set up work whereas SAN is an ordinary SSL certificate but with the subject alternative name field utilized. Because of this I would recommend the SAN certificate.