We report on rheo-optical experiments performed with an entangled asymmetric polystyrenepolyisoprene diblock copolymer solution in dioctyl phthalate (DOP), in the regime of pretransitional fluctuations. The combined information extracted from optical signals under steady and transient flows suggests the stress enhancement of fluctuations in the flow direction and their subsequent suppression at higher stresses in the plane normal to the velocity gradient direction. The viscoelastic signature of these structural changes resulting from the complex interplay between fluctuations and the shear flow includes an initial shear thinning regime followed by an abrupt shear thickening and then an apparent viscosity plateau. At even higher stresses, the flow curve displays a second shear thinning, and eventually a second viscosity plateau is reached. The corresponding optical response indicates that the copolymer solution is driven toward a dynamic phase separation, in a way similar to a semidilute polymer solution sheared below the theta point. However, no flow instability is detected at the highest stresses because the shear-induced structure relaxes too fast when compared to the longest relaxation time exhibited by the quiescent disordered copolymer solution.