A three-dimensional ionospheric reconstruction system is presented that models ionospheric dynamics and accounts for well-known limitations in the available data by using geometrically transformed prior models based on available models, such as the Parameterized Ionospheric Model (PIM) or the International Reference Ionosphere (IRI), to produce density solutions consistent with available Total Electron Content (TEC) measurement data. It is known that current state of the art prior density models, such as PIM or IRI, can only simulate a statistical mean ionosphere. As a result, sudden variations in ionospheric electron density will not be represented in these models. This paper focuses on a three-dimensional ionospheric density reconstruction system that uses a set of geometrical transformations to produce Flexible Prior Models (FPM). The Flexible Prior Model process allows means to include flexibility in a prior model in the form of geometrical variations that are not well represented in current state-of-the-art ionospheric prior density models. The updated priors are used as initial solution models for a set of (A, B) Multiplicative Algebraic Reconstruction Technique (ABMART) algorithms, that can easily incorporate additional information and provide a spatially constrained density solution, consistent with the available data and our current knowledge of ionospheric dynamics. The ultimate goal is to create a three-dimensional adaptive ionospheric electron density reconstruction system that would make it possible to generate real-time ionospheric maps supported by available TEC data. Such maps would be of significant utility in predicting and correcting the impact of electron density gradients and irregularities on radio waves.