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The MTX-based compounds are promising rare-earth-free candidates for multicaloric applications due to the proximity of their structural and magnetic phase transitions. In this paper, we use first principles calculations to study how chemical pressure affects the energetics, saturation magnetization, and volume change. Our calculations reveal the presence of a complex interplay between the M-, T-, and X-site elements in tuning the properties. The choice of elements for rational alloy design should be informed by the site-specific response. Our work motivates future synthesis and characterization efforts to focus on uncovering site-specific data to tailor strategies for maximizing the caloric response and bridge the knowledge-gap.