In this research study, the synthesis of poly lactic acid (PLA) based bio composite material factors contributions were investigated through the Taguchi-based grey relational analysis (GRA) technique. Effects of micro crystalline cellulose (MCC) and montmorillonite (MTT) nano clay filler, sorbitol (S) plasticizer, and temperature (T) operating factor on the PLA matrix through melt-mixing preparation method. The tensile strength (TS), Young modulus (YM), flexural strength (FS), flexural modulus (FM), hardness, impact strength (IS), water absorption (WA), and density properties of bio composite material were investigated for each experimental setup (orthogonal array, L16). Additionally, neat PLA and optimal sample structural, thermal, and morphological properties were examined through Fourier transform infrared spectroscopy (FTIR), X-Ray diffraction (X-RD), thermal gravimetry analysis/differential thermal gravimetry (TGA/DTG), and DSC and SEM analyses. The obtained result for optimal mechanical and physical properties of MCC/MTT/S/PLA bio composite was MCC at level 3 (6%), MTT at level 4 (9%), S at level 2 (10%), and T at level 4 (175 °C). Analysis of variance (ANOVA) shows that MTT has the greatest significant effect on mechanical and physical properties of MCC/MTT/S/PLA bio composite followed by MCC, T, and S. The confirmation test indicates that the improvement of weighted grey relational grade (GRG) from 0.7896 to 0.846 and the FTIR, XRD, thermal gravimetry/differential scanning calorimetry (TG/DSC), and scanning electron microscopy (SEM) results indicates that the good interaction between PLA and fillers, improvement of thermal and morphological properties of optimal (6MCC/9MTT/10S/175 °C) bio composite samples. Therefore, the multi-response characteristics of MCC/MTT/S/PLA bio composite can be highly improved by this technique.