Following the reports of candidate chiral doublet bands observed in odd-$A$ cesium isotopes, the triaxial deformations with corresponding configuration and the possible multiple chiral doublet ($\mathrm{M}\ensuremath{\chi}\mathrm{D}$) phenomenon in $^{125,127,129,131}\mathrm{Cs}$ are investigated within the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations. The existence of the $\mathrm{M}\ensuremath{\chi}\mathrm{D}$ phenomenon in $^{125,129,131}\mathrm{Cs}$ is demonstrated and expected based on different high-$j$ particle-hole configurations and triaxial deformations.