Energy-dispersive X-ray spectroscopy (EDXS) mapping with a scanning transmission electron microscope (STEM) is commonly used for chemical characterization of materials. However, STEM-EDXS quantification becomes challenging when the phases constituting the sample under investigation share common elements and overlap spatially. In this paper, we present a methodology to identify, segment, and unmix phases with a substantial spectral and spatial overlap in a semi-automated fashion through combining non-negative matrix factorization with a priori knowledge of the sample. We illustrate the methodology using a sample taken from an electron beam-sensitive mineral assemblage representing Earth's deep mantle. With it, we retrieve the true EDX spectra of the constituent phases and their corresponding phase abundance maps. It further enables us to achieve a reliable quantification for trace elements having concentration levels of similar to 100 ppm. Our approach can be adapted to aid the analysis of many materials systems that produce STEM-EDXS datasets having phase overlap and/or limited signal-to-noise ratio (SNR) in spatially-integrated spectra.