You can do this by "chaining" call handlers together for that - have the operator handler use supervised transfer (i.e. "wait for answer") for the first extension and have the greeting set to blank and the after greeting action go to "attemp transfer for" the next call handler configured to do a supervised transfer for the next phone and so on.
Make sure all handlers are using the altnerate transfer and alternate greeting so schedules wont matter and such when setting this up (alternate rules are always active regardless of schedule).
this is a little awkward to do in Unity but you can make it work - it's better to leverage the phone system's call queuing capabilities - Unity's not really designed for this and you can chew up your ports pretty easily doing this, but you can make it work.
