Lamellae forming CEC triblock and CECEC pentablock copolymers located near the order-disorder transition temperature were subjected to reciprocating shear as a function of strain amplitude and thermal history. Both variables strongly influence the mix of perpendicular vs parallel lamellae alignment in the triblock copolymer, while only the strain amplitude significantly affects the pentablock material. Dramatically different responses of CEC vs CECEC to shear are rationalized on the basis of viscoelastic contrast and nonlinear chain stretching, each operating differently on the initially disordered and ordered states.