  A novel class of achievable rate regions is obtained for the K-receiver
broadcast channel with two groupcast messages. The associated achievability
schemes are parameterized by an expansion of the message set which then
determines how random coding techniques are employed, which include generalized
versions of {\em up-set} message-splitting, the generation of possibly multiple
auxiliary codebooks for certain compositions of split messages using
superposition coding, partial interference decoding at all receivers, and joint
unique and non-unique decoding.
  New capacity results are established for certain partially ordered classes of
general broadcast channels for certain two non-nested messages. Moreover, when
specialized to the combination network (CN), some of the inner bounds are
shown, via converse results, to result in the capacity region for (a) the two
messages intended for two sets of K-1 receivers each and (b) two nested
messages in which one message is intended for one or (c) two (common)
receivers. In the latter two cases, we hence recover previous results by
Bidokhti et al obtained therein using network coding schemes based on
rate-splitting and linear superposition coding. Furthermore, we show the
achievability of rate pairs in two examples of CNs, with three and four common
receivers each, used in the previous literature to show the sub-optimality of
rate-splitting and linear superposition coding, and to motivate a pre-encoding
technique and a block-Markov linear superposition coding for the CN, with the
latter then lifted to the general broadcast channel. Our results suggest that
the proposed framework here, when specialized to the CN, is strong enough to
incorporate the enhancements afforded by those two latter techniques, thereby
suggesting among other things, that perhaps block-Markov superposition coding
is not necessary for the general broadcast channel.
