In an older Stackoverflow thread (https://stackoverflow.com/questions/20450676/will-using-http-and-https-on-the-same-domain-affect-seo) I learned that you can run two different websites from the same domain one with an HTTP protocol and the other with an HTTPS protocol. My web host says this doesn't work.
My example http://www.csd-i.org https://www.csd-i.org
The reason that I want to do this is that I want to split our somewhat old website in half. One half (the HTTP half) would be the existing membership portion of the site - for which I don't want to have to change all the link URLs. The second half (the HTTPS half) would be a modern version of the public side of the website that would have an SSL certificate and would be mobile responsive.
Question one: does it work?
Question two: how does one set this up?