Electrospinning bears great potential for the manufacturing of scaffolds for tissue engineering, consisting of a porous mesh of ultrafine fibers that effectively mimic the extracellular matrix (ECM) and aid in directing stem cell fate. However, for engineering purposes, there is a need to develop material-by-design approaches based on predictive models. In this methodological study, a rational methodology based on statistical design of experiments (DOE) is discussed in detail, yielding heuristic models that capture the linkage between process parameters (Xs) of the electrospinning and scaffold properties (Ys). Five scaffolds made of polycaprolactone are produced according to a 22-factorial combinatorial scheme where two Xs, i.e., flow rate and applied voltage, are varied between two given levels plus a center point. The scaffolds were characterized to measure a set of properties (Ys), i.e., fiber diameter distribution, porosity, wettability, Young’s modulus, and cell adhesion on murine myoblast C1C12 cells. Simple engineering DOE models were obtained for all Ys. Each Y, for example, the biological response, can be used as a driver for the design process, using the process-property model of interest for accurate interpolation within the design domain, enabling a material-by-design strategy and speeding up the product development cycle. The implications are also illustrated in the context of the design of multilayer scaffolds with microstructural gradients and controlled properties of each layer. The possibility of obtaining statistical models correlating between diverse output properties of the scaffolds is highlighted. Noteworthy, the featured DOE approach can be potentially merged with artificial intelligence tools to manage complexity and it is applicable to several fields including 3D printing.