We study both experimentally and theoretically the self-assembly of binary polycaprolactone–polyethylene oxide (PCL–PEO) block copolymers in dilute solution, where self-assembly is triggered by changing the solvent from the common good solvent THF to the selective solvent water, and where the two species on their own in water form vesicles and spherical micelles respectively. We find that in water the inter-micellar exchange of these block copolymers is extremely slow so that the resultant self-assembled structures are in local but not in global equilibrium (i.e., they are non-ergodic). This opens up the possibility of controlling micelle morphology both thermodynamically and kinetically. Specifically, when the two species are first molecularly dissolved in THF before mixing and self-assembly (‘pre-mixing’) by dilution with water, the morphology of the formed structures is found to depend on the mixing ratio of the two species, going gradually on a route of decreasing surface curvature from vesiclesvia an intermediate regime of micelles in the shape of ‘bulbed’ rods, rings, Y-junctions and finally to spherical micelles as we increase the proportion of the “sphere formers”. On the other hand, if the two species are first partially self-assembled (by partial exchange of the solvent with water) before mixing and further self-assembly (‘intermediate mixing’), novel metastable structures, including nanoscopic ‘pouches’, emerge. These experimental results are corroborated by Self-Consistent Field Theory (SCFT) calculations which reproduce the sequence of morphologies seen in the pre-mixing experiments. SCFT also reveals a clear coupling between polymer composition and aggregate curvature, with regions of positive and negative curvature being stabilized by an enrichment and depletion of sphere formers respectively. Our study demonstrates that both thermodynamic and kinetic blending of block copolymers are effective design parameters to control the resulting structures and allow us to access a much richer range of nano-morphologies than is possible with monomodal block copolymer solutions.