  We report the observation of tens of minor lines of the combinational
spin-flip Raman scattering in a CdTe:Mn quantum well by means of the
high-resolution optical spectroscopy. Classification of this manifold leads to
four characteristic values of energy, that correspond to four different types
of pair clusters of Mn ions: the nearest, second, third etc. neighbors. All the
four energies show up in a single experiment with a very high precision,
providing experimental grounds for a deeper understanding of the d-d exchange
interactions in a diluted magnetic semiconductor and demonstrating the capacity
of the employed method. The major (nearest-neighbor) exchange constant J_1 =
6.15 K was found to consent with its previously reported value. Other detected
characteristic energies are as follows: J_{(2)} = 1.80 K, J_{(3)} = 1.39 K,
J_{(4)} = 0.81 K.
