The Starlink satellites launched on 3 February 2022 were lost before they fully arrived in their designated orbits. The loss was attributed to two moderate geomagnetic storms that occurred consecutively on February 3-4. We investigate the thermospheric neutral mass density variation during these storms with the Multiscale Atmosphere-Geospace Environment (MAGE) model, a first-principles, fully coupled geospace model. Simulated neutral density enhancements are validated by Swarm satellite measurements at the altitude of 400-500 km. Comparison with standalone TIEGCM and empirical NRLMSIS 2.0 and DTM-2012 models suggests better performance by MAGE in predicting the maximum density enhancement and resolving the gradual recovery process. Along the Starlink satellite orbit in the middle thermosphere (∼ 200 km altitude), MAGE predicts up to 150% density enhancement near the second storm peak while standalone TIEGCM, NRLMSIS 2.0 and DTM-2012 suggest only ∼ 50% increase. MAGE also suggests altitudinal, longitudinal, and latitudinal variability of storm-time percentage density enhancement due to height dependent Joule heating deposition per unit mass, thermospheric circulation changes, and travelling atmospheric disturbances. This study demonstrates that a moderate storm can cause substantial density enhancement in the middle thermosphere. Thermospheric mass density strongly depends on the strength, timing, and location of high-latitude energy input, which cannot be fully reproduced with empirical models. A physics-based, fully coupled geospace model that can accurately resolve the high-latitude energy input and its variability is critical to modeling the dynamic response of thermospheric neutral density during storm time.