  We have studied the three-body recombination rates on both sides of the
interspecies d-wave Feshbach resonance in the $^{85}$Rb\,-$^{87}$Rb-$^{87}$Rb
system using the $R$-matrix propagation method in the hyperspherical coordinate
frame. Two different mechanisms of recombination rate enhancement for positive
and negative $^{85}$Rb\,-$^{87}$Rb d-wave scattering lengths are analyzed. On
the positive scattering length side, the recombination rate enhancement occurs
due to the existence of three-body shape resonance, while on the negative
scattering length side, the coupling between the lowest entrance channel and
the highest recombination channel is crucial to the appearance of the
enhancement. In addition, our study shows that the intraspecies interaction
plays a significant role in determining the emergence of recombination rate
enhancements. Compared to the case in which the three pairwise interactions are
all in d-wave resonance, when the $^{87}$Rb-$^{87}$Rb interaction is near the
d-wave resonance, the values of the interspecies scattering length that produce
the recombination enhancement shift. In particular, when the
$^{87}$Rb-$^{87}$Rb interaction is away from the d-wave resonance, the
enhancement disappears on the negative interspecies scattering length side.
