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The Modified Quasichemical Model in the Pair Approximation (MQMPA) can effectively capture the thermodynamic features of a binary solution with Short-Range Ordering (SRO). If the model is used to treat a ternary solution, a geometric interpolation method must be employed to extend the bond energy expression from binary to ternary formalism. The aim of the present work is to implement such extension by means of a generic geometric interpolation approach. The generic method is unbiased and can be transformed into the widely used Kohler, Toop and Muggianu approaches with special interpolation parameters. The interpolation parameters can be calculated by the integration method as well as be optimized by ternary experimental data. The generic bond energy formalism (GBEF) has thus been derived to provide the MQMPA great flexibility to describe ternary solutions with complex configurations. Moreover, the GBEF is more concise than the formula derived by a combinatorial Kohler-Toop method. The concise GBEF is in the respect more conveniently programmed. Eventually, the Cu-Li-Sn liquid where both SRO and clustering among atoms occur is employed to validate the effectiveness and reliability of the GBEF within the MQMPA.