Piling on some Service Fabric-specific info to Eli's answer: Yes you can do all of this and use an http.sys-based self-hosted web server to host multiple sites using different host names on a single VIP, such as Katana or WebListener in ASP.NET Core 1.
The piece to this that is currently missing in Service Fabric is a way to configure the hostname in your endpoint definition in ServiceManifest.xml. Service Fabric services run under Network Service by default on Windows, which means the service will not have access to create a URL ACL for the URL it wants to open an endpoint on. To help with that, when you specify an HTTP endpoint in an endpoint definition in ServiceManifest.xml, Service Fabric automatically creates the URL ACL for you. But currently, there is no place to specify a hostname, so Service Fabric uses "+", which is the strong wildcard that matches everything.
For now, this is merely an inconvenience because you'll have to create a setup entry point with your service that runs under elevated privileges to run netsh to setup the URL ACL manually.
We do plan on adding a hostname field in ServiceManifest.xml to make this easier.