The current framework that we use to model our universe is the FLRW model of the universe given by the FLRW metric in general relativity. This model has 1 unique singularity at co-moving time $t=0$. There are no other singularities in this model of the universe (it's not a fine-grained enough model that singularities like those inside black holes would show up within this model). Since there's only the 1 singularity in this model, our current understanding of the universe does not really permit a secondary "Big Bang" occurring as an "event" within our universe.
Your question runs into a few other issues such as "how do you define 'a big bang'?". The concept of a big bang singularity originated from within the FLRW model where it is unique. If you have other models of the universe (or multi-verse) - how would you define what's a "big bang" within them?
From a more general point of view with regards to multiverse theories, all I can really say is that the concept of a "multiverse" is, at this time, purely speculative from a physics perspective.