Aluminum gallium arsenide has highly desirable properties for integrated parametric optical interactions: large material nonlinearities, maturely established nanoscopic structuring through epitaxial growth and lithography, and a large band gap for broadband low-loss operation. However, its full potential for record-strength nonlinear interactions is only released when the semiconductor is embedded within a dielectric cladding to produce highly confining waveguides. From simulations of such, we present second and third order pair generation that could improve upon state-of-the-art quantum optical sources and make novel regimes of strong parametric photon-photon nonlinearities accessible.