Virtual server to support two https site each on different domain

IS APM involved at all? Is this just LTM? I will try and answer this without all of the details though you can use an iRule to direct requests based on host, URI, etc. to different pools, you can create local traffic policies as well as use Server Name Indication (SNI) to identify different https sites on a single VS. Hope this helps.

SNI Use Case: https://support.f5.com/csp/article/K13452

About Local Traffic Policies: https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/bigip-local-traffic-policies-getting-started-13-1-0/1.html

iRule example below.

 when HTTP_REQUEST { 
  switch [HTTP::host] { 
    www.example1.com { pool pool1 } 
    www.example2.com { pool pool2 } 
    www.example3.com { pool pool3 } 
    default { pool default_pool }
  } 
}