How might fully saturated benzene polymers of composition [(CH)(6)](n) form under high pressure? In the first approach to answering this question, we examine the stepwise increase in saturation of a one-dimensional stack of benzene molecules by enumerating the partially saturated polymer intermediates, subject to constraints of unit cell size and energy. Defining the number of four-coordinate carbon atoms per benzene formula unit as the degree of saturation, a set of isomers for degree-two and degree-four polymers can be generated by either thinking of the propagation of partially saturated building blocks or by considering a sequence of cycloadditions. There is also one 4 + 2 reaction sequence that jumps directly from a benzene stack to a degree-four polymer. The set of degree-two polymers provides several useful signposts toward achieving full saturation: chiral versus achiral building blocks, certain forms of conformational freedom, and also dead ends to further saturation. These insights allow us to generate a larger set of degree-four polymers and enumerate the many pathways that lead from benzene stacks to completely saturated carbon nanothreads.