Hot melt extrusion (HME) is a common manufacturing process used in the pharmaceutical industry to improve the solubility of poorly soluble active pharmaceutical ingredients (API). The goal is to create an amorphous solid dispersion (ASD) where the amorphous form of the API is stabilized within a polymer matrix. Traditionally, the development of pharmaceutically approved polymers has focused on requirements such as thermal properties, solubility, drug–polymer interactions, and biocompatibility. The mechanical properties of the material have often been neglected in the design of new polymers. However, new downstream methods require more flexible polymers or suitable plasticizer polymer combinations. In this study, two grades of the polymer polyvinyl alcohol (PVA), which is already established for HME, are investigated in terms of their mechanical, rheological, and thermal properties. The mechanical properties of the extruded filaments were tested by the three-point bending test. The rheological behavior was analyzed by oscillating plate measurements. Thermal analysis was performed by differential scanning calorimetry (DSC). In addition, the solid and liquid plasticizers mannitol, sorbitol, triacetin, triethyl citrate, polyethylene glycol, and glycerol were evaluated for use with PVA and their impact on the polymer properties was elaborated. Finally, the effects of the plasticizers are compared to each other, and the correlations are analyzed statistically using principal component analysis (PCA). Thereby, a clear ranking of the plasticizer effects was established, and a deeper understanding of the polymer–plasticizer interactions was created.