A single concentration solution (36 vol %) of a symmetric polystyrene-block-polyisoprene, total molecular weight 30 000, in the styrene-selective solvent diethyl phthalate shows a remarkably rich sequence of thermotropic order-order transitions (OOT). A combination of small-angle X-ray scattering measurements both under quiescent conditions and after shear orientation, supplemented with rheology and static birefringence, indicates the following phase sequence. At room temperature the solution adopts a close-packed lattice of spherical micelles, corresponding to a mixture of face-centered-cubic (fee) and hexagonally close-packed (hcp) phases. At approximately 60°C the solution undergoes a "partial" OOT, in that the fee portion transforms to body-centered-cubic (bcc), whereas the hep domains persist. At approximately 82°C the hcp/bcc mixture transforms to hexagonally packed cylinders, and finally the cylinder phase undergoes the order-disorder transition at 113°C. Through the use of two different shear cells, scattering patterns along both shear gradient and vorticity axes were obtained. These data confirmed that all three OOTs (fee to bcc, bcc to cylinder, and hep to cylinder) are epitaxial. The first two follow the pathways previously established, whereas the hcp to cylinder is described for the first time in block copolymers. Among the other novel features of this system are the proximity to a triple line (coexistence of hep, bcc, and cylinders) at 82°C.