We observed high-order 2- to 4-photon photoemission and above threshold photoemission (ATP) processes with 3.07 eV light from the Cu(001) surface. The intensity of 3-photon photoemission via excitation through the n=1 image potential state significantly exceeded that of the 2-photon process. The ATP occurs either via single photon transitions from the image potential resonances above the vacuum level or by multiphoton transitions from image potential states below the vacuum level. The experimental ratio of the m- to (m+1)-photon process yields is sensitive to the electronic band structure of the solid.