The generalization of polarization beating quasi-phase matching (PBQPM) and of multi-mode quasi-phase matching (MMQPM) for the generation of high-order harmonics is explored, and a novel method for achieving polarization beating is proposed. If two (and in principle more) modes of a waveguide are excited, modulation of the intensity, phase, and/or polarization of the guided radiation will be achieved; by appropriately matching the period of this modulation to the coherence length, quasi-phase-matching of high harmonic radiation generated by the guided wave can occur. We show that it is possible to achieve efficiencies with multi-mode quasi-phase matching greater than the ideal square wave modulation. We present a Fourier treatment of QPM and use this to show that phase modulation, rather than amplitude modulation, plays the dominant role in the case of MMQPM. The experimental parameters and optimal conditions for this scheme are explored.Please note that this is an arXiv version of the original APS paper. Please cite original paper L. Z. Liu, K O'Keeffe, and S. M. Hooker, Phys. Rev. A 87, 023810 (2013). APS link here: http://pra.aps.org/abstract/PRA/v87/i2/e023810