In this paper, we study delivery of two nested message sets over combination networks with an arbitrary number of receivers, where a subset of receivers (public receivers) demand only the lower priority message and a subset of receivers (private receivers) demand both the lower and the higher priority messages. We give a complete rate region characterization over combination networks with three public and many private receivers, where achievability is through linear coding. Our encoding scheme is general and characterizes an achievable region for arbitrary number of public and private receivers.