And if it were, would it constitute an expanding bubble in our universe - with a definite (expanding) surface.
That would be nice - none of this irritating "everywhere is the centre and there is no edge" business...
But would it have the mass of our universe concentrated in a small (to start with) space? That would cause problems to our space-time fabric, wouldn't it?
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.
