We demonstrate the existence of stable collective excitation in the form of "supersolitons" propagating through chains of solitons with alternating signs (i.e., Newton's cradles built of solitons) in nonlinear optical couplers, including the PT -symmetric version thereof. In the regular coupler, stable supersolitons are created in the cradles composed of both symmetric solitons and asymmetric ones with alternating polarities. Collisions between moving supersolitons are investigated too, by the means of direct simulations in both the regular and PT -symmetric couplers.