Monitoring website with different header packets

As of LTMv9, multiple instances of the same pool member can be independently monitored.

If I understand your requirements correctly, I think the best way to accomplish what you're after is to create 3 separate pools, all with the same members, and monitor each with a single Host-header specific monitor:

VS:80
  resource:  rule=pick_a_pool_by_Host_header
pool site_x
  member 10.1.1.1:80
  member 10.1.1.2:80
  monitor app_x (sends site_x-specific host header)
pool site_y
  member 10.1.1.1:80
  member 10.1.1.2:80
  monitor app_y (sends site_x-specific host header)
pool site_z
  member 10.1.1.1:80
  member 10.1.1.2:80
  monitor app_z (sends site_x-specific host header)

HTH

/deb