Ternary blended cements, such as limestone calcined clay cement (LC3), represent a type of strategic binder for the mitigation of environmental impacts associated with cement production. These are estimated to reduce CO2 emissions by about 40% compared to ordinary Portland cement (OPC). In this paper, we explore the possibility of producing such ternary blends by utilizing secondary raw materials that may be locally available. Specifically, the primary limestone that is commonly used in LC3 is herein substituted with quarry dust obtained by sourcing “kunkur”, a carbonaterich sedimentary rock (also known as caliche) that can be locally utilized for the production of ordinary OPC clinker. To optimize the blending proportions of ternary cement consisting of OPC, calcined clay, and kunkur fines, a “design of experiment” (DoE) approach was implemented with the goal of exploring the possibility of reducing the amount of the OPC fraction to values lower than 50%. The properties of the formulated blends were assessed by a combination of techniques that comprise mechanical strength testing, XRD time-dependent quantitative phase analysis, and SEM–EDS microstructural and microchemical analyses. The results suggest that ternary blended cement based on kunkur fines forms hydration products, such as hemicarboaluminates, which are also observed in LC3. This shows that such waste materials can potentially be used in sustainable cement blends; however, the presence of kaolinite in the kunkur fines seems to affect their strength development when compared to both OPC and conventional LC3.