If the universe ends is it part of something even biggger?
There are at least a couple of ways of discussion this.
1) The somewhat silly way. That is to point out the universe might be (or is) defined as everything. In which case, by definiton, it isn't part of something bigger. I don't think that's all that interesting.
2) The other is to take the "universe" as everything we see and all the rest that we expect is a continuation of this. It might be sort of "everything that originated with the big bang".
In the second case there might be something else beyond. A new idea about colliding "branes" moving in multidimensional space would have our "universe" being just one of these branes. The big bang happened when our collided with another. The whole framework is conjectured to have always existed without beginning or end. This is conjecture and fun cosmological speculation more than anything else (or at least that's what I understand right now).
I have know idea if this will ever be testable in any sensible way. Some individuals talk about "thinking outside the box". HA! They don't have any idea of just how far outside some of the cosmologists think! None at all.