  In this article, we will construct the additional perturbative quantum torus
symmetry of the dispersionless BKP hierarchy basing on the $W_{\infty}$
infinite dimensional Lie symmetry. These results show that the complete quantum
torus symmetry is broken from the BKP hierarchy to its dispersionless
hierarchy. Further a series of additional flows of the multicomponent BKP
hierarchy will be defined and these flows constitute an $N$-folds direct
product of the positive half of the quantum torus symmetries.
