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As an important strengthening phase in Al-Mg-Fe alloy, the elastic and ductile–brittle characteristics of Al₁₃Fe₄ intermetallics hold prime significance in ascertaining the mechanical properties and potential application of Al-Mg-Fe alloys. In this study, multialloying of Co, Cu, Cr, Mn, and Ni has been adopted for tuning the mechanical characteristics of the Al₁₃Fe₄ phase; their effects on mechanical features and electronic structure of the Al₁₃Fe₄ phase have been scrutinized systematically by first-principles calculations employing the density functional theory. The replacement of Fe with M (M = Co, Cu, Cr, Mn, and Ni) is energetically advantageous at 0 K, as evidenced by the negative cohesive energy and mixing enthalpy of all Al₁₃(Fe,M)₄ phases. Cu and Ni, on the contrary, have a detrimental impact on Al₁₃Fe_4′s modulus and hardness due to the evolution of chemical bonding strength. Co, Cr, and Mn are thus, interesting candidate elements. In the light of <i>B</i>/<i>G</i> and Poisson’s ratio (<i>σ</i>) criteria, Al₁₃Fe₄, Al₁₃(Fe,Cu)₄, and Al₁₃(Fe,Ni)₄ have superior ductility; however, Al₁₃(Fe,Co), Al₁₃(Fe,Mn), and Al₁₃(Fe,Cr)₄ tend to be brittle materials. Calculation-based findings show that Co, Cr, and Mn are appropriate alloying elements for enhancing fracture toughness, whereas Mn reduces Al₁₃Fe_4′s elastic anisotropy. The electronic structure assessment found that the mechanical properties of the intermetallics are predominantly influenced by the Al-M bonds when the alloying element M replaced Fe.