Can I supply unicast and multicast from same enoder stream?

For live events, we currently send two streams from the on-site encoder to the Adobe Media Server.  One is for unicast clients and one is for multicast clients.  All of this occurs on our internal WAN, and works perfectly fine.  However, we have been contacted about conducting a live event from a very bandwidth constrained site, and this has me wondering if there is a way I can send just one stream from the encoder and have the AMS sort it out into unicast and multicast output streams.

Is there a way to do this?

Thank you.