Collective dynamics and force generation by cytoskeletal filaments are crucial in many cellular processes. Investigating growth dynamics of a bundle of N independent cytoskeletal filaments pushing against a wall, we show that ATP/GTP hydrolysis leads to a collective phenomenon that is currently unknown. Obtaining force-velocity relations for different models that capture chemical switching, we show, analytically and numerically, that the collective stall force of N filaments is greater than N times the stall force of a single filament. Simulating growing actin and microtubule bundles, considering both sequential and random hydrolysis, we make quantitative predictions of the excess forces.