Yes, it seems likely that if were referring to some finite set of properties to define a universe (such as some finite volume of space or finite and precise set of physical properties), then there would have to at least potentially be more, though time itself provides dynamics that could potentially connect between these (maybe another way of looking at that would be that memory can span multiple finite states).

I think the capability for such dynamics to exist would have to itself be an innate and timeless attribute of oneself, though 'oneself' is not necessarily even fundamentally singular but could exist as a composite of all things compatible with that property - just like all motions witnessed in space can be compared by common units of time. Those units don't define anything specific except that there is a singular "Now" and that changes occur in relationship to a singular form of space defined by its properties observed "Here".

There are many possible ways in which things could be organized compatibly beyond immediate visibility and I assume that they could all be considered equally valid - as an analogy with the ocean description above - how many different subsets of that infinite ocean could contain the bottle? Well there would be an (in some ways even larger) infinite number of ways of constructing various volumes of that ocean that contained the bottle - the bottle doesn't really exist within a specific ocean, but instead many possible oceans - it's always in whatever version is presently realized. That singular aspect of realization appears to be innate property of time and that asymmetry is also likely what allows for the perception of the rest to appear as extensive and infinite (you can't have many things without something that defines what one is, in order to denote that there is specifically not one of something).

Anyway, it seems that no matter how you try to describe it, there's fundamentally no way to remove ones own (innate) influence, even if it's in terms of distributed abilities (a good example of that is the body itself, a comprised of many cells - the capabilities of the body as a whole arise from the collective abilities of all the cells and what properties they share in common that allow them to act in a singular fashion - yes, even if it's purely coincidence. I guess if there's an "infinite" quantity of "stuff" such coincidences could be rather much guaranteed).

The closest thing to a symmetrical version that appears possible is simply that everything does what it wants (the asymmetry would remain that ones own ability to be a part of that would have to be innate).

Consider this, if the innate natural of some original state was to become or acquire some other state, then that foundational impulse/drive/motive would appear to never be altered by any subsequently acquired/experienced state and if all of these additions were placed into the same context as the original state, then this would appear to be continual pressure to be/experience something "else".

Now let's say that such an entity comes along and happens to encounter a state that desires to remain unchanged . In that case, there would be a conflict in placing it within the original context and it would appear such a state would have to remain "external" to that origin in some sense.

If we have a set of laws by which these motions occur (for example, we might want to place all these into the context of a memory that we can rewind. In that case, all of these need to be retained in a specific order and a manner to "navigate" through that space of past experiences would need to be present and this would resemble physical laws in the sense of being reversible) and these motions must continually encounter new states, then we could see this form of motion similar to space filling. Here's an analogy from the movie Tron:



We could analogize these "trails" as past events in spacetime.

Now if we happened to, for example, encounter a specific state in this space and desired to remain in similar conditions, then this would be similar to a continual spiralling outward away from that state. So eventually circumstances would push things in other directions (there's actually a way to look at gravity as repulsive instead of attractive - distances are relative. A uniform expansion or contraction aren't actually detectable)

With more references or dimensions involved that outward pressure could be greatly slowed though (imagine, for example, that you added a new dimension of motion and could then reduce the significance of that outward pressure - for example, a motion away from some point in 1 dimension occurs at maximum velocity, whereas in 2 dimension a spiral moving away at a rate of 1/t occurs, in 3 dimensions this rate is 1/(t^2) instead and much slower. With multiple references to orbit between, the rate can be decreased)

But ultimately it would appear that any finite set of properties or dimensions can't constrain such pathways to remaining within finite distances over an infinite time.

There's a different way of potentially doing things though if we look instead at the forms and manners of growth in a relative manner though. In that case, you could, for example, multiplex a single timeline into two timelines in parallel - each follows the other and their forms are extended in spacetime identically relative to each other (except for a displacement in time and the specific present qualities present in each "Now").

There are lots of other interesting possibilities, but it appears trying to "orbit" any specific finite set of properties may not lead to long term satisfaction ... just another consideration (besides, those Tron bike games could get tiring after a while).

BTW, speaking of bottles and time ... (sounds like this guy enjoys a fine aged wine )