  In this paper we study the gauge invariance of the third quantized
super-group field cosmology which is a model for multiverse. Further, we
propose both the nfinitesimal (usual) as well as the finite
superfield-dependent BRST symmetry transformations which leave the effective
theory invariant. The effects of finite superfield-dependent BRST
transformations on the path integral (so-called void functional in the case of
third quantization) are implemented. Within the finite superfield-dependent
BRST formulation, the finite superfield-dependent BRST transformations with
specific parameter switch the void functional from one gauge to another. We
establish this result for the most general gauge with the help of explicit
calculations which holds for all possible sets of gauge choices at both the
classical and the quantum levels.
