  The influence of a saturable nonlinearity on the modulation instability in
oppositely directed coupler in the presence of high-order effects is
investigated. By using the standard linear stability analysis, we obtain the
instability gain that exhibits a significant change in the bands of instability
due to the effects of a saturable nonlinearity. We also show that even in the
presence of saturation there is no change in instability gain when we compare
the results obtained for both channels not influenced by self-steepening effect
or for both channels influenced by self-steepening effect but opposite in sign.
Regarding the Raman effect, there is reflection symmetry (asymmetry) to the
gain at zero perturbation frequency when the values of the Raman coefficients
in each directional coupler are equal and with same (opposite) sign. For the
anomalous group velocity dispersion regime we observe that the growth of the
saturation parameter is followed by an increase in the null gain region near
{\Omega} = 0, enlarging the separation of the instability bands close to this
point. Finally, we show that an efficient control of the modulation instability
can be realized by adjusting self-steepening effect and intrapulse Raman
scattering, even in the presence of a saturable nonlinearity.
