The engineering of new 3D bioprinting approaches has shown great promise in the field of tissue engineering and disease modelling. However, the high cost of commercial 3D bioprinters has limited their accessibility, especially to those laboratories in resource-limited settings. Moreover, the need for a 3D bioprinting system capable of dispensing multiple materials is growing apace. Therefore, the development of a Microfluidic-assisted Open Source 3D bioprinting System (MOS3S) for the engineering of hierarchical tissues is needed to progress in fabricating functional tissues, but with a technology accessible to a wider range of researchers. The MOS3S platform is designed to allow the deposition of biomaterial inks using microfluidic printheads or coaxial nozzles for the in-situ crosslinking and scaffolds fabrication. The coupling of 3D printed syringe pumps with the motion control system is used for driving the tunable extrusion of inks for the fabrication of centimeter scale hierarchical lattice constructs for tissue engineering purposes. MOS3S performance have been validated to fabricate high-resolution structures with coaxial microfluidic technology, opening to new frontiers for seminal studies in pre-clinical disease modelling and tissue regeneration.