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 technology. MEW has the hitherto unrealized potential of fabricating 3D porous interconnected fibrous mesh-patterned scaffolds in conjunction with cellular-relevant fiber diameters and inter-fiber distances without the use of cytotoxic organic solvents. However, this potential cannot be readily fulfilled due to the large number and complex interplay of the multivariate independent parameters of the melt electrospinning process. To overcome the challenge, dimensional analysis was employed to identify a "Printability Number" (NPR), which correlated with the dimensionless numbers arising from the non-dimensionalization 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 towards efficient printability. Experimental investigations using a poly(e-caprolactone) melt have indeed revealed that any perturbations arising from an imbalance between the downstream and the upstream resistive forces can be eliminated by systematic tuning of Vp and Q for prescribed thermal conditions. This, in concert with appropriate tuning of the translational stage speed, has enabled steady state equilibrium conditions to be achieved for the printing of microfibrous woven meshes with precise and reproducible geometries.