We study the reducibility of a class of nonlinear quasi-periodic systems near an elliptic equilibrium point with multi-dimensional Liouvillean basic frequencies, and investigate the existence of response solutions for such systems. Under a non-resonance condition weaker than the Brjuno condition, which allows for a class of multi-dimensional Liouvillean frequencies, we prove via the KAM method that for most sufficiently small parameters, the system can be reduced to a system with zero as its equilibrium point, and thus the original system admits the corresponding response solutions.