Magnetic excitations of long-range ordered localized spin systems are generally well described by the linear spin-wave theory which accounts for phase fluctuations of the order parameter. In contrast, quasiparticles associated with amplitude fluctuations are only observed in a few quantum antiferromagnets close to a quantum critical point (QCP), where the ordered moment is suppressed significantly from its fully saturated value. Via inelastic neutron scattering measurements and extended spin-wave calculations, we present the observation and explanation of amplitude modes in the magnetic excitation spectra of three-dimensional S=3/2 spin dimers Cr2TeO6 and Cr2WO6, which nevertheless are away from the QCP with the ordered moment reduced by only ∼24%. We show that the large spin of Cr3+ and narrow bandwidth of the amplitude modes render their detection even in polycrystalline samples. This paper suggests that amplitude modes are not the privilege of ordered spin systems in the vicinity of a QCP, but may be common excitation modes that can survive even away from the QCP, paving a way to search for and understand the physics of amplitude fluctuations in antiferromagnets beyond the quantum spin limit (S=1/2).