The aim of this work was to investigate the effect of process parameters on the printability of a formulation containing copovidone and paracetamol, and on the properties of solid oral forms 3D-printed through selective laser sintering. Firstly, the influence of the heating temperature was evaluated individually, and it was revealed that this parameter was critical for printability, as a sufficiently high temperature (100 °C) is necessary to avoid curling. Secondly, the effects of laser power, scan speed, and layer thickness were determined using a Box–Behnken design. The measured responses, printing yield, height, weight, hardness, disintegration time, and percentage of drug release at 10 min showed the following ranges of values: 55.6–100%, 2.92–3.96 mm, 98.2–187.2 mg, 9.2–83.4 N, 9.7–997.7 s, and 25.8–99.9%, respectively. Analysis of variance (ANOVA) proved that the generated quadratic models and the effect of the three–process parameters were significant (p < 0.05). Yield improved at high laser power, low scan speed, and increased layer thickness. Height was proportional to laser power, and inversely proportional to scan speed and layer thickness. Variations in the other responses were related to the porosity of the SOFs, which were dependent on the value of energy density. Low laser power, fast scan speed, and high layer thickness values favored a lower energy density, resulting in low weight and hardness, rapid disintegration, and a high percentage of drug release at 10 min. Finally, an optimization was performed, and an additional experiment validated the model. In conclusion, by applying a Quality by Design approach, this study demonstrates that process parameters are critical for printability, but also offer a way to personalize the properties of the SOFs.