Using a combinatorial screening method based on the self-consistent-field theory for polymers, we study the bulk morphology and the phase behavior of pi-shaped ABC block copolymers, in which A is the backbone and B and C are the two grafts. By systematically varying the positions of the graft points, the pi-shaped block copolymer can change from a star block copolymer to a linear ABC block copolymer. Thus, the corresponding order-order phase transition due to the architecture variation can be investigated. At two given compositions, we find seven different morphologies ("three-color" lamellar phase, "three-color" hexagonal honeycomb phase, lamellae with beads inside, dodecagon-hexagon-tetragon, hexagon-hexagon, lamellae with alternating beads, and octagon-octagon-tetragon). The hexagon-hexagon morphology has not been reported previously for linear and star triblock copolymers in the bulk state. The phase diagram of the pi-shaped ABC block copolymer with symmetric interactions among the three species is constructed. When the volume fractions of block B and block C are equal, the triangle phase diagram shows reflection symmetry. When the shorter block is fixed at the backbone end and the other block moves to the other end along the backbone, the resulting morphology reaches to the same as that of a linear triblock copolymer rapidly. These results may help the design of the microstructures of complex block copolymers.