Magnetic reconnection drives multispecies particle acceleration broadly in space and astrophysics. We perform the first 3D hybrid simulations (fluid electrons, kinetic ions) that contain sufficient scale separation to produce nonthermal heavy-ion acceleration, with fragmented flux ropes critical for accelerating all species. We demonstrate the acceleration of all ion species (up to Fe) into power-law spectra with similar indices, by a common Fermi acceleration mechanism. The upstream ion velocities influence the first Fermi reflection for injection. The subsequent onsets of Fermi acceleration are delayed for ions with lower charge-mass ratios (Q/M), until growing flux ropes magnetize them. This leads to a species-dependent maximum energy/nucleon ∝(Q/M)^{α}. These findings are consistent with in situ observations in reconnection regions, suggesting Fermi acceleration as the dominant multispecies ion acceleration mechanism.