To make the sound absorber easy to fabricate and convenient for practical application, a modular composable acoustic metamaterial with multiple nonunique chambers (MCAM-MNCs) was proposed and investigated, which was divided into a front panel with the same perforated apertures and a rear chamber with a nonunique grouped cavity. Through the acoustic finite element simulation, the parametric studies of the diameter of aperture d, depth of chamber T0, and thickness of panel t0 were conducted, which could tune the sound absorption performances of MCAM-MNCs-1 and MCAM-MNCs-2 for the expected noise reduction effect. The effective sound absorption band of MCAM-MNCs-1 was 556 Hz (773-1329 Hz), 456 Hz (646-1102 Hz), and 387 Hz (564-951 Hz) for T = 30 mm, T = 40 mm, and T = 50 mm, respectively, and the corresponding average sound absorption coefficient was 0.8696, 0.8854, and 0.8916, accordingly, which exhibited excellent noise attenuation performance. The sound absorption mechanism of MCAM-MNCs was investigated by the distributions of the total sound energy density (TSED). The components used to assemble the MCAM-MNCs sample were fabricated by additive manufacturing, and its actual sound absorption coefficients were tested according to the transfer matrix method, which demonstrated its feasibility and promoted its actual application.