Is there another universe which is made up of antimatter, in large amounts like ours is made up of matter?

There are various theories about how the matter anti-matter asymmetry arose. See this search for lots of related questions. It's generally believed that the Big Bang formed almost equal quantities of matter and anti-matter, but there was a very small inbalance i.e. there was slightly more matter. The anti-matter all annihilated with matter to leave normal matter and lots of photons (the particle to photon ratio in the universe is about $10^{-9}$, that is a billion photons for each particle of matter).

Over the years various ideas have been proposed, for example that some areas of the universe contain matter and other areas contain anti-matter. However no-one has ever come up with a convincing theory to describe how this could happen. You suggest there could be an anti-matter universe, but you'd need to put this on a sound mathematical footing for anyone to take the suggestion seriously, and no-one has ever managed to do this.

By contrast the suggestion I mentioned in my first paragraph is theoretically plausible, though the exact mechanism for generating the small excess of matter is unknown. It requires a process known as CP violation, and this is known to happen and has been measured at accelerators. However the amount of CP violation we've measured is too small to account for all the matter we see. It's widely believed that when we understand physics beyond the Standard Model, be it String Theory or whatever, we'll discover how the excess of matter originated.

A universe is by definition all there is, so there is only one of 'em. Yet be my guest to imagine any number of them as long as they are disconnected from the one we are actually in.

I know this post is old, but I actually had this same idea about the other side being antimatter when I read this article https://www.pbs.org/wgbh/nova/article/big-bounce/ I know the argument posted there is disputed, and I am in no place to prove the math, but if the other side is antimatter in equal quantities as our side is matter it preserves CPT and avoids CP violation, if I am not mistaken this is actually exactly what CPT predicts. And it seems plausible given that antimatter in some respects is a mirror of its matter particle, i.e. opposite charge, spin, etc. so opposite time would not be unreasonable, but again this is disputed and not proven, but long story short you are not far off from some real research gong on into this exact idea. In my experience though it is a touchy subject to many theoretical and experimental physicists.

I believe that your intuition is sound. I am also learning about CPT symmetry.

The CPT transformation turns our universe into its "mirror image" and vice versa.

The implication of CPT symmetry is that a "mirror-image" of our universe — with all objects having their positions reflected through an arbitrary point (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (corresponding to a charge inversion) — would evolve under exactly our physical laws.

This means there is a distinction between a universe such as ours that is predominantly matter and its "mirror-image" that is predominantly anti-matter. However, we can't tell which one we are in. Granted, there would be such a pairing at every point and every plane containing that point. Still, there is a sense in which we can speak of two mirror universes.

Given that both possibilities are equally valid, shouldn't we suppose that, in fact, they are both true? Consequently, it would be straightforward that there is no reason for matter-antimatter to be balanced in a single universe, as it is balanced within the pair. In other words, it would be expected that one universe would have a preponderance of matter and the other of anti-matter. Whereas the Wikipedia article on charge conjugation raises a false problem:

The C-symmetry is particularly troublesome, physically, as the universe is primarily filled with matter, not anti-matter, whereas the naive C-symmetry of the physical laws suggests that there should be equal amounts of both. It is currently believed that CP-violation during the early universe can account for the "excess" matter, although the debate is not settled.

I suppose that it's much less presumptuous to suppose that there are dual universes, one of which is mostly matter and the other anti-matter, rather than to suppose that there are dual possible universes, one of which exists and the other not at all. The latter is like presuming that there is no back side to the moon if we haven't seen it. It's a general principle of quantum mechanics that all paths are taken, that all possibilities are true.

One consequence of your intuition is that we would not have to invent mechanisms to explain why a balanced universe doesn't have all the matter and antimatter annihilate, or to explain the observed imbalance. A more physical consequence is that if we suppose the matter-antimatter imbalance from the start, then the parameter expressing that imbalance can be a key ingredient in models of the unfolding of the universe. Indeed, if we suppose an imbalance from the start, then there may be a natural value for the degree of imbalance. For example, if we studied random matrices with n real eigenvalues, n odd, so that the number of positive and negative eigenvalues naturally differs, then we can calculate the likely distributions of the eigenvalues.