We report on the observation of up to 16 PR (paramagnetic resonance) Raman lines due to collective multiple spin flips within the Zeeman split ⁶S_5/2 ground state of the Mn²⁺ ion in a quantum well structure with semimagnetic wells of Cd_0.98Mn_0.02Te and nonmagnetic barriers of Cd_0.76Mg_0.24Te with applied magnetic fields B ≤ 7.5T. This large number was observed close to resonance with the heavy hole (HH) dipole transitions of the narrowest quantum well (18angstrom) in Voigt backscattering geometry. We suppose that these transitions are allowed by the lowering of the symmetry provided by the heterostructure and an exchange magnetic field produced by the heavy holes. The in-plane component of the total angular momentum of all magnetic ions which interact with the photoexcited heavy hole is not generally conserved. A model is presented which yields good fits to the experimental data.