The totality of all universes appears to increase exponentially according to the latest physics, except that the increase is in the number of universes rather than the size of any one universe. The size of any one universe is expected to expand forever, so that size is not so important as number.

We are currently incapable of proving the existence of other universes, because we have no way of contacting them. In fact, most peer reviewed journals I've read have said that even if such a hypotheses were true, there would never be any way to prove it.
The "totality" of our universe is increasing, IF you mean the overall size by totality. Our universe however is not gaining any mass, because no new matter is being formed.

On the other hand this process has apparently been going on forever, and so there is already an infinite number of universes and an infinite amount of consciousness, whatever that means. And the process will probably go on forever, or at least for the lifetime of Braham, which from our perspective is essentially forever. So it`s fairly clear what man`s immediate contribution to this process is, but one wonders at the ultimate goal of the whole thing.

Again, there is no evidence whatsoever for a multiverse theory. There is also no evidence that the cycle of our own universe has gone on forever or will continue to go on. Recent calculations have shown that our universe’s inflation has not slowed down enough for gravity to be strong enough to cause the Big Crunch. It is currently more likely that our universe will continue to expand until it is so cold that nothing can live in it. The theory that the universe is constantly exploding and reconstituting back into period-sized point only to explode again is currently in jeopardy. As far as we know, we are the only universe ever to be. There's no way to prove that a universe ever came "before" us.