Constructing multi-source satellite-derived water quality (WQ) products in inland and nearshore coastal waters from the past, present, and future missions is a long-standing challenge. Despite inherent differences in sensors' spectral capability, spatial sampling, and radiometric performance, research efforts focused on formulating, implementing, and validating universal WQ algorithms continue to evolve. This research extends a recently developed machine-learning (ML) model, i.e., Mixture Density Networks (MDNs) (Pahlevan et al., 2020; Smith et al., 2021), to the inverse problem of simultaneously retrieving WQ indicators, including chlorophyll-a (Chla), Total Suspended Solids (TSS), and the absorption by Colored Dissolved Organic Matter at 440 nm (acdom(440)), across a wide array of aquatic ecosystems. We use a database of in situ measurements to train and optimize MDN models developed for the relevant spectral measurements (400-800 nm) of the Operational Land Imager (OLI), MultiSpectral Instrument (MSI), and Ocean and Land Color Instrument (OLCI) aboard the Landsat-8, Sentinel-2, and Sentinel-3 missions, respectively. Our two performance assessment approaches, namely hold-out and leave-one-out, suggest significant, albeit varying degrees of improvements with respect to second-best algorithms, depending on the sensor and WQ indicator (e.g., 68%, 75%, 117% improvements based on the hold-out method for Chla, TSS, and acdom(440), respectively from MSI-like spectra). Using these two assessment methods, we provide theoretical upper and lower bounds on model performance when evaluating similar and/or out-of-sample datasets. To evaluate multi-mission product consistency across broad spatial scales, map products are demonstrated for three near-concurrent OLI, MSI, and OLCI acquisitions. Overall, estimated TSS and acdom(440) from these three missions are consistent within the uncertainty of the model, but Chla maps from MSI and OLCI achieve greater accuracy than those from OLI. By applying two different atmospheric correction processors to OLI and MSI images, we also conduct matchup analyses to quantify the sensitivity of the MDN model and best-practice algorithms to uncertainties in reflectance products. Our model is less or equally sensitive to these uncertainties compared to other algorithms. Recognizing their uncertainties, MDN models can be applied as a global algorithm to enable harmonized retrievals of Chla, TSS, and acdom(440) in various aquatic ecosystems from multi-source satellite imagery. Local and/or regional ML models tuned with an apt data distribution (e.g., a subset of our dataset) should nevertheless be expected to outperform our global model.