The X-ray absorption spectrum of copper was studied using two different experimental techniques. Discontinuities with energies corresponding to the double excitation 1s^-- and to the triple excitation 1s^--+2s^- and 1s^--+2p^- were observed and studied. The magnitudes of these discontinuities were compared with that of the K absorption edge of the element, to determine the cross section for the simultaneous creation of two and three electronic vacancies, resulting from the absorption of a single X-ray photon. These were only a fraction of one per cent of the 1s^- single-electron cross section. The measured energies of the observed discontinuities are in good agreement with the results obtained on the basis of Hartree-Fock calculations for the corresponding multielectron excitations and fall within the limits of the uncertainties in the final results.