Atom scattering from physisorbed overlayers is first briefly reviewed. While good agreement has been obtained between measurements and calculations both for diffraction scans and selective adsorption [H. Jónsson, J. H. Weare, T. H. Ellis, G. Scoles and U. Valbusa, Phys. Rev. B, 1984, 30, 4203; T. H. Ellis, G. Scoles, U. Valbusa, H. Jónsson and J. H. Weare, Surf. Sci., 1985, 155, 499; H. Jónsson, J. H. Weare, T. H. Ellis and G. Scoles, in preparation; J. M. Hutson and C. Schwartz, J. Chem. Phys., 1983, 79, 5179], detailed information on the scattering potential has not been inferred from the experimental data because of three highly correlated unknowns in the theoretical potential: (1) uncertainty in the probe–adatom pair potential, (2) uncertainty in the probe–substrate potential and (3) non-additive many-body corrections. New close-coupling calculations are presented here for the scattering of He from a commensurate overlayer of Kr on graphite and compared with recent selective adsorption data of Larese et al.(J. Z. Larese, W. Y. Leung, D. R. Frankl, N. Holter, S. Chung and M. W. Cole, preprint). This is a favourable system in that the He–Kr pair potential is well known and a semiempirical helium–graphite potential consistent with extensive experimental data on clean graphite has recently been constructed (H. Jónsson and J. H. Weare, in preparation). Good agreement is obtained when the theoretical potential only contains two-body contributions, but it is significantly improved by shifting the lowest bound-state energy by –0.12 meV. The long-range triple-dipole correction alone is frequently used to represent the total non-additive correction, e.g. in calculations of the binding energy of rare-gas solids. When applied to the present problem, the triple-dipole correction shifts the lowest bound state in the wrong direction by +0.16 meV. A correction due to thermal vibration further shift this level by +0.07 meV. There is, therefore, a 0.35 meV difference between the lowest bound-state energy of this theoretical potential and the experimental value. We estimate the uncertainty in the two-body terms [(1) and (2)] to be ±0.1 meV. Typically the uncertainty due to experimental parameters is estimated to be ±0.1 meV. The data therefore suggest that the total non-additive correction is not well represented by the long-range triple-dipole correction alone and that other many-body corrections of opposite sign need to be included. Three-body corrections to the short-range repulsive interaction have not been quantitatively estimated but are known to be attractive [W. J. Meath and R. A. Aziz, Mol. Phys., 1984, 52, 225).