The ability of multiblock ABC terpolymers to self-assemble into multicompartment micelles in an A-selective solvent is of great current interest. We have used dissipative particle dynamics (DPD) to explore the morphologies adopted by a particular block terpolymer architecture, A 2-star-(B-alt-C), where the two A blocks form the micelle corona and the alternating B and C blocks segregate within the core. Parameters of interest include the strength of the pairwise interactions among A, B, and C, the relative length of the A blocks compared to B + C, and the relative selectivity of the solvent towards B and C. A rich suite of structures are observed, including those with either spherical or wormlike cores, and with internally segregated B and C domains. Within the spherical micelle family, the B and C domains adopt various packings, including concentric layers, the "hamburger" motif (B-C-B layers and C-B-C layers), and a bicontinuous network. For wormlike micelles, the B and C domains are arranged as stacked alternating disks, or as intertwined helices. The choice of morphology is rationalized in terms of the relative block volume fractions and interaction energies. The DPD algorithm is a promising approach to screen ABC terpolymer architectures for the ability to produce potentially useful hierarchical structures.