The carburizing and nitriding, essential surface modification methods for steels, enhance wear, fatigue, and corrosion resistance by forming fine carbides, nitrides, and nanoclusters involving alloy elements. Understanding the interactions between interstitial X (C or N) and substitutional elements M is critical for optimizing these processes and tailoring the material properties to specific applications. This study investigates the interaction energies in diatomic and triatomic clusters involving C/N atoms and substitutional elements of Al, Si, Ti, V, Cr, Mn, Co, Ni, Cu, Zr, Nb, and Mo. Using the first-principles calculations, this study reveals the intricate balance of interactions within these clusters, highlighting how atomic arrangements and specific element combinations can lead to either repulsion or attraction. We found that the interaction energies for triatomic clusters can be represented using a linear combination of interaction energies for diatomic clusters. Stable triatomic clusters comprise the second nearest neighbor M–X interactions for Fe–Ti–N, Fe–V–N, and Fe–Nb–N alloys. This finding was consistent with experimental observations of the monolayer clusters. Our analysis using the multiple linear regression and stratified analysis reveals that the metallic radius of element M influences interaction in M–X clusters: a larger metallic radius causes repulsion in the first nearest neighbor clusters and attraction in the second and third nearest neighbor clusters due to strain relief.