Consider two random vectors X1 and X2 whose distributions are defined according to the multivariate frailty approach, and let Xk,t=[Xk−t|Xk>t], k=1,2, be the corresponding vectors of residual lifetimes at . Conditions for multivariate stochastic comparisons of random vectors described by the frailty approach have been recently presented in Misra et al. (2009). Here we prosecute their study, providing sufficient conditions for the stochastic comparison X1,t≤stX2,t, where t is an arbitrary vector in Rn. Sufficient conditions for the stochastic comparisons Xi,t≤stXi,t+v, where t is as above and v is a vector with non-negative components, are presented too.