This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite units. Here I continue on to the construction of iterable units and disembedding. Finally, I look at the role of the stages of unit construction in making additive and multiplicative coordinations. Throughout I link terms used by various learning researchers. [For Part 1, see EJ1084354.]