The rapid development of miniaturized satellite instrument technology has created a new opportunity to deploy constellations of passive microwave (PMW) radiometers to permit retrievals of the same Earth scene with very high temporal resolution to monitor cloud evolution and processes. For such a concept to be feasible, it must be shown that it is possible to distinguish actual changes in the atmospheric state from the variability induced by making observations at different Earth incidence angles (EIAs). To this end, we present a flexible and physical optimal estimation-based algorithm designed to retrieve profiles of atmospheric water vapor, cloud liquid water path, and cloud ice water path from cross-track PMW sounders. The algorithm is able to explicitly account for the dependence of forward model errors on EIA and atmospheric regime. When the algorithm is applied to data from the Temporal Experiment for Storms and Tropical Systems Technology Demonstration (TEMPEST-D) CubeSat mission, its retrieved products are generally in agreement with those obtained from the similar but larger Microwave Humidity Sounder instrument. More importantly, when forward model brightness temperature offsets and assumed error covariances are allowed to change with EIA and sea surface temperature, view-angle-related biases are greatly reduced. This finding is confirmed in two ways: through a comparison with reanalysis data and by making use of brief periods in early 2019 during which the TEMPEST-D spacecraft was rotated such that its scan pattern was along track, allowing dozens of separate observations of any given atmospheric feature along the satellite’s ground track.