Three-dimensional bioprinting is a promising field in regenerating patient-specific tissues and organs due to its inherent capability of releasing biocompatible materials encapsulating living cells in a predefined location. Due to the diverse characteristics of tissues and organs in terms of microstructures and cell types, a multinozzle extrusion-based 3D bioprinting system has gained popularity. The investigations on interactions between various biomaterials and cell-to-material can provide relevant information about the scaffold geometry, cell viability, and proliferation. Natural hydrogels are frequently used in bioprinting materials because of their high-water content and biocompatibility. However, the dominancy of liquid characteristics of only-hydrogel materials makes the printing process challenging. Polycaprolactone (PCL) is the most frequently used synthetic biopolymer. It can provide mechanical integrity to achieve dimensionally accurate fabricated scaffolds, especially for hard tissues such as bone and cartilage scaffolds. In this paper, we explored various multimaterial bioprinting strategies with our recently proposed bio-inks and PCL intending to achieve dimensional accuracy and mechanical aspects. Various strategies were followed to coprint natural and synthetic biopolymers and interactions were analyzed between them. Printability of pure PCL with various molecular weights was optimized with respect to different process parameters such as nozzle temperature, printing pressure, printing speed, porosity, and bed temperature to coprint with natural hydrogels. The relationship between the rheological properties and shape fidelity of natural polymers was investigated with a set of printing strategies during coprinting with PCL. The successful application of this research can help achieve dimensionally accurate scaffolds.