Altering the content of an alloying element in alloy materials will inevitably affect the content of other elements, while the effect is frequently disregarded, leading to subsequent negligence of the common influence on the physical properties of alloys. Therefore, the correlation between alloying elements and physical properties has not been adequately addressed in the existing studies. In response to this problem, the present study focuses on the Al10Ti15Nix1Crx2Cox3 alloys and investigates the competitive interplay among Ni, Cr, and Co elements in the formation of physical properties through a single-element (SE) analysis and a multi-element (ME) analysis based on the first principles calculations and the partial least squares (PLS) regression. The values of C11 and C44 generally increase with the incorporation of Ni or Cr content in light of SE analysis, which is contrary to the inclination of ME analysis in predicting the impact of Ni and Cr elements, and the Ni element demonstrates a pronounced negative competitive ability. The overall competitive relationship among the three alloying elements suggests that increasing the content of Ni and Cr does not contribute to enhancing the elastic constants of alloys, and the phenomenon is also observed in the analysis of elastic moduli. The reason is that the SE analysis fails to account for the aforementioned common influence of multiple alloying elements on the physical properties of alloys. Therefore, the integration of SE analysis and ME analysis is more advantageous in elucidating the hidden competitive mechanism among multiple alloying elements, and offering a more robust theoretical framework for the design of alloy materials.