We systematically investigate multiphoton absorption as a polarization-resolved nonlinear optical probe of planar altermagnets (ALMs). We show that the angular harmonic of the altermagnetic spin splitting fixes the lowest optical absorption at which a symmetry-selective response appears: two-photon absorption for d-wave order, four-photon absorption for g-wave order, and six-photon absorption for i-wave order. In each case, there exists a polarization channel locked to the symmetry harmonic of the altermagnetic texture in which the direct n-photon contribution to the transition matrix element is absent. This changes the frequency scaling of the absorption rate relative to other polarization channels and provides a direct optical fingerprint of the underlying altermagnetic harmonic. Our results establish a hierarchy of nonlinear spectroscopic signatures that distinguishes d-, g-, and i-wave altermagnetic spin splittings beyond linear response.