An nb initio static exchange approach is devised for calculations of the core-electron shake phenomenon of large species. The approach employs appropriately spin-coupled two-hole potentials for the various shakeup/ shakeoff channels. It is far extendable in the number of atoms treated, in the one-particle basis set, and in the spectral range, while restricted in correlation to full intrachannel correlation. Using cluster modeling it is implemented for shake spectra of molecules adsorbed on surfaces. A demonstration is given for the oxygen and carbon shake spectra of COCuN, N=0,14,50, modeling CO/Cu(100). The reduction of shake energies and the accompanying increase in intensity are well recovered by the large cluster employed (COCu50), while the small cluster (COCu14) could only recover half the total shakeup/shakeoff intensity created by the absorption. An assignment of the strong low-lying shakeup states could be obtained in terms of orbital excitations and in terms of local versus delocalized characters of these excitations. Results for the oxygen and carbon shakeup spectra of free carbon monoxide are analyzed in some detail in view of data from high-resolution experiments and from other theoretical approaches.