Previous studies have reported that the partitioning of Re to the $\gamma^\prime$ phase in Ni-Al-Re alloys is reversed to the $\gamma$ matrix in commercial multicomponent superalloys. We employ density functional theory calculations to study the reversal of Re partitioning and investigate the interaction between Re-X, with X=Ta, Ti, W, Cr and Co in Ni-based  $\gamma$(fcc) and  $\gamma^\prime$(L1$_2$). The partitioning of Re is analyzed with varying X concentrations from 1 to 12.5 at.% in the Ni- $\gamma^\prime$ phase. Our results reveal that Ta and W, which have a stronger partitioning tendency to  $\gamma^\prime$ than Re in model ternary Ni-Al-X alloys, suppress the partitioning of Re in  $\gamma^\prime$, and reverse Re partitioning to the  $\gamma$ phase at higher Ta/W concentration. First-principles calculations also show large differences in substitutional energies of solutes in the  $\gamma$ phase between ferro-magnetic and non-magnetic states. The partitioning coefficients computed from the non-magnetic state are consistent with experimental observations at high temperature, while the result from the ferro-magnetic calculations indicate a strong partitioning of Re, Ta, W and Ti to  $\gamma^\prime$ precipitates at low temperature.