The direct electrostatic printing of highly viscous thermoplastic polymers onto movable collectors, a process known as melt electrospinning writing (MEW), has significant potential as an additive biomanufacturing (ABM) technology. MEW has the hitherto unrealized potential of fabricating three-dimensional (3D) porous interconnected fibrous mesh-patterned scaffolds in conjunction with cellular-relevant fiber diameters and interfiber distances without the use of cytotoxic organic solvents. However, this potential cannot be readily fulfilled owing to the large number and complex interplay of the multivariate independent parameters of the melt electrospinning process. To overcome this manufacturing challenge, dimensional analysis is employed to formulate a “Printability Number” (NPR), which correlates with the dimensionless numbers arising from the nondimensionalization of the governing conservation equations of the electrospinning process and the viscoelasticity of the polymer melt. This analysis suggests that the applied voltage potential (Vp), the volumetric flow rate (Q), and the translational stage speed (UT) are the most critical parameters toward efficient printability. Experimental investigations using a poly(ε-caprolactone) (PCL) melt reveal that any perturbations arising from an imbalance between the downstream pulling forces and the upstream resistive forces can be eliminated by systematically tuning Vp and Q for prescribed thermal conditions. This, in concert with appropriate tuning of the translational stage speed, enables steady-state equilibrium conditions to be achieved for the printing of microfibrous woven meshes with precise and reproducible geometries.