Estimating global and multi-level Thermosphere Neutral Density (TND) is important for studying coupling processes within the upper atmosphere, and for applications like orbit prediction. Available models fall short in predicting realistic TND changes due to the simplicity of model structure or sampling limitations. In this study, a simultaneous Calibration and Data Assimilation (C/DA) algorithm is applied to integrate freely available CHAMP, GRACE, and Swarm derived TND measurements into the NRLMSISE-00 model. The improved model, called `C/DA-NRLMSISE-00', and its outputs fit to these measured TNDs, are used to produce global TND fields at arbitrary altitudes (with the same vertical coverage as the NRLMSISE-00). Seven periods, between 2003-2020 that are associated with relatively high geomagnetic activity selected to investigate these fields, within which available models represent difficulties to provide reasonable TND estimates. Independent validations are performed with along-track TNDs that were not used within the C/DA framework, as well as with the outputs of other models such as the Jacchia-Bowman 2008 and the High Accuracy Satellite Drag Model. The numerical results indicate an average 52%, 50%, 56%, 25%, 47%, 54%, and 63% improvement in the Root Mean Squared Errors of the short term TND forecasts of C/DA-NRLMSISE00 compared to the along-track TND estimates of GRACE (2003, altitude 490 km), GRACE (2004, altitude 486 km), CHAMP (2008, altitude 343 km), GOCE (2010, altitude 270 km), Swarm-B (2015, altitude 520 km), Swarm-B (2017, altitude 514 km), and Swarm-B (2020, altitude 512 km), respectively.