The geometric and electronic structures of [Mn44+Mn3+3(µ3-L2 -)3(µ3-X -(OAc) - 3(dbm) -3] (L = O, X = F, dbmH = dibenzoyl-methane) molecule has been studied by first-principles calculations. It was shown in our previous paper that the ferrimagnetic structure of Mn$^{4 + }$Mn$^{3 + }_{3}$ molecules is determined by the $\pi $ type hybridization between the $d_{z^2}$ orbitals at the three high-spin Mn$^{3 + }$ ions and the $t_{2g}$ orbitals at the Mn$^{4 + }$ ion by the $p$ orbitals at the $\mu _{3}$-L$^{2 - }$ ions. To design new Mn$^{4 + }$Mn$^{3 + }_{3}$ molecules having much more stable ferrimagnetic state, one approach is suggested. That is controlling the Mn$^{4 + }$-($\mu _{3}$-L$^{2 - })$-Mn$^{3 + }$ exchange pathways by rational variation in $\mu _{3}$-L ligands to strengthen the hybridization between Mn ions. By this ligand variation, $J_{AB}$ can be enhanced by a factor of 3. Our results should facilitate the rational synthesis of new single-molecule magnets.