Bioprinting for regenerative medicine has been gaining a lot of popularity in today's world. Despite being one of the rigorously studied fields, there are still several challenges yet to be solved. Geometric fidelity and mechanical complexities stand as roadblocks when it comes to the printability of the customized constructs. Exploring the rheological properties of the compositions helps us understand the physical and mechanical properties of the biomaterials which are closely tied to the printability of the filament and eventually, geometric fidelity of the constructs. To ensure the structural integrity of the constructs, viscosity enhancers such as carboxymethyl cellulose (CMC) and crosslinkers like CaCl2 and CaSO4 were used. These crosslinkers can be used before (precrosslinking) and after (postcrosslinking) the extrusion of considered compositions to investigate and compare the outcome. To do this, mixtures of CMC (viscosity enhancer), Alginate, and CaCl2 and CaSO4 (crosslinkers) were prepared at various concentrations maintaining minimum solid content (≤8%). Each composition was subjected to a set of rheological tests like flow curve for shear thinning behavior, three points thixotropic for recovery rate, and amplitude test for gelation point. Various geometric fidelity identification tests were conducted and correlated with their physical properties. Some compositions were used to fabricate large-scale constructs (in cm-scale) to demonstrate their capability. This research is a thorough investigation of compositions when they are introduced to crosslinkers and viscosity enhancers which can be crucial for the 3D printing world.