This research focuses on selectively precipitating impurities, namely aluminum, iron, and thorium, from a pregnant leach solution (PLS) rich in rare earth elements (REEs). The main aim is to remove these impurities while retaining the maximum possible REE in solution, a vital step in REE processing. The study combines experimental work with modeling to decode the complex precipitation patterns. A design of experiments and response surface methodology are employed to evaluate how temperature, pH adjustment (using 20 wt% magnesium carbonate (MgCO3)), and oxidation using hydrogen peroxide (H2O2) affect impurity removal and REE preservation. Characterization of the resulting solid precipitates is performed using X-ray diffraction (XRD), Raman spectroscopy, and scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDX). Analysis shows that precipitates at pH 3 and 5.5 mainly comprise ferrihydrite, aluminum sulfate, and magnesium carbonate. EDX also reveals REEs in these precipitates. This research sheds light on the process of selectively removing impurities from REE solutions and lays a foundation for enhancing REE recovery, thus supporting sustainable and cost-effective production of these essential materials. The findings inform the development of more effective and environmentally benign REE production methods, crucial for many high-tech applications. Further studies and process enhancements based on this work could improve REE recovery efficiency, meeting the growing industry demand for these materials.