The deformations and the corresponding configurations of the odd-odd As isotopes are investigated using the adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) theory. Energy minima with triaxial deformations and high-j particle-hole configurations are obtained in 72,74,76,78,80As, where the chiral doublet bands are possible to appear. The existence of multiple chiral doublet (MχD) is demonstrated in 74,76,78As. Based on the calculated single-particle levels, we also find possible coexistence of chiral and pseudospin symmetries in the odd-odd As isotopes.