You can "daisy chain" call handlers together like this no problem... Here's how I would do it.
Create three call handlers (A, B and C) and set their alternate transfer rule to be active and have them to supervised transfers to their respective extension numbers. Set their alternate greetings active (this way you don't have to worry about schedules or which rule will fire, the alternate rule always over rides all others). For the greeting of A set it to the "blank" option and for the After Greeting Action set it to "attempt transfer for" call handler B. Similiarly for call handler B, set it's alternate greeting rule to "blank" and have it's after greeting action set to "attempt transfer" to call handler C.... and so on. In the last call handler of the chain you'll want to take play a proper greeting and play a message or the like.
I've had folks loop such chains to they continue to try extensions forever - this is not a good idea, I wouldn't do that. If you chain several handlers together, it might be a good idea to have short greetings for A and B etc... above that tell the user you're still trying, please hold on or the like since if the extensions are RNA the pause on their end could be pretty long if you have several handlers in a row doing this - they might think the system hung up on them if they don't have hold music to keep them company.
