Anionic polymerization for the preparation of polystyrene-b-polybutadiene is well-established and leads to thermoplastic elastomers on industrial scale. The classical ABA block copolymer (BCP) architecture and composition usually forms a cylindrical morphology in the bulk state. Their anisotropic mechanical properties are, however, unfavorable for many applications. The gyroid microphase is entirely isotropic, but it is only formed in a narrow compositional area of around 35 vol% of the minority polymer block. In the present study, a second-generation dendrimer-like block copolymer structure ((AB)2B)3 is described. This BCP architecture is expected to show a higher curvature on the microphase boundaries, which leads to a larger morphological range for the gyroid phase. Three compositionally different polymers are synthesized by living anionic polymerization strategies and the resulting morphology is analyzed via transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS). The dendrimer-like BCPs are compared to their less branched analogues, namely the asymmetric star polymers and H-shape stars. The expected influence of the dendrimer-like BCP architecture on the microphase separation is investigated paving the way to a promising synthetic platform for interesting mechanical and optical properties.