The naturally layered colossal magnetoresistive (CMR) manganites La (sub2-2x) Sr (sub1+2x) Mn (sub 2) O (sub 7) exhibit an extremely varied range of magnetic and electronic behavior over a very narrow composition range between x=O.3 and x=0,5, The successful synthesis in our laboratories of compounds with nominally greater than 50 percent Mn (sup 4+) concentration has now allowed the study of this heretofore unexplored region of the phase diagram. Here we present detailed neutron diffraction measurements of these compounds with doping levels 0.5 less than x less than 1.0. As predicted by simple theories, the type-A layered antiferromagnetic (AF) structure is found at x approximately O.5 and the type-G 'rocksalt' AF structure at x equals l.O. Between these two extremes is found a C-type structure (ferromagnetic rods parallel to b coupled antiferromagnetically to all neighboring rods) stabilized by orbital ordering of y (sup2) states. Also in this Mn (sup 4+) -rich regime is found a region in which no long-range magnetic order is observed. We discuss how semi-empirical models can explain the variety of magnetic structures and how structural trends as a function of doping corroborate the unifying notion of a shift from in-plane to axial orbital occupation as the Mn (sup 4+) I concentration is decreased.