  The relevance of neglecting three- and four-body interactions in the
coarse-grained version of the Asakura-Oosawa model is examined. A mapping
between the first few virial coefficients of the binary nonadditive hard-sphere
mixture representative of this model and those arising from the coarse-grained
(pairwise) depletion potential approximation allows for a quantitative
evaluation of the effect of such interactions. This turns out to be especially
important for large size ratios and large reservoir polymer packing fractions.
