This research work reports the usability of binary additive materials known as tile waste dust (TWD) and calcined kaolin (CK) in ameliorating the mechanical response of weak soil. The extreme vertex design (EVD) was adopted for the mixture experimental design and modelling of the mechanical properties of the soil-TWD-CK blend. In the course of this study, a total of fifteen (15) design mixture ingredients’ ratios for water, TWD, CK and soil were formulated. The key mechanical parameters considered in the study showed a considerable rate of improvement to the peak of 42%, 755 kN/m2and 59% for California bearing ratio, unconfined compressive strength and resistance to loss in strength respectively. The development of EVD-model was achieved with the aid of the experimental derived results and fractions of component combinations through fits statistical evaluation, analysis of variance, diagnostic test, influence statistics and numerical optimization using desirability function to analyze the datasets. In a step further, the non-destructive test explored to assess the microstructural arrangement of the studied soil-additive materials displayed a substantial disparity compared to the corresponding original soil material and this is an indicator of soil improvement. From the geotechnical engineering perspective, this study elucidates the usability of waste residues as environmental friendly and sustainable materials in the field of soil re-engineering.