I don't have any experience with physics. I am just very interested to know whether or not this might be possible.
It seems to me that your question is ill-posed.
With that I mean that the question is not well defined: take for example the classic problem
"If a tree falls but no one is there, does it make any sound?"
The problem with this is the unclear definition of "sound", so if one does not define it better, the question is ill-posed.
Back to your problem.
Let's say you have a number of oranges (may be one, may be infinite). These oranges can have a lot of properties; may be blue, green, yellow, big, small, etc., whatever you may think.
But no orange has the property "there are infinite oranges". It is not a property of the orange, it is a property of their "container", so to speak.
To be more precise, let A be the set of all the oranges. The property "there are infinitely many oranges" is not a property of a particular orange, it is a property of the set A (namely, the set A has infinitely many elements)
Now substitute orange with universe.
You can see now that your question is ill-posed: in your title, you are implying that the property "there are infinitely many universes" is a property of a particular universe, but this is not the case
It's not entirely clear to me what you mean by 'realities', but I'm going to assume that you mean something like possible worlds, either in the sense of Everettian quantum mechanics (given that you mention physics) or in the sense of possible worlds as used in the semantics of modal logic (see the Stanford Encyclopedia of Philosophy article – this is a good article to read for questions related to this issue ).
(Let's put aside for the moment how many possible worlds there are (such as whether, as you suggest in your question, there are infinitely many).)
Now, if we think that there are possible worlds, we will think that different things are true at different possible worlds. So, for example, at the actual world, it is true that I am answering a question on Stack Exchange, but, since I might have decided to use this time otherwise, there is a possible world at which it is false that I am answering a question on Stack Exchange.
Your question is then, I take it, something like this: Suppose there are non-actual possible worlds; that is, at the actual world, it is true that there are non-actual worlds. Are there possible worlds (or is it consistent that there be) possible worlds at which it is false that there are (other) possible worlds?
Here are a few ways in which we could answer the question:
Although at different possible worlds, different objects exist (e.g. I exist in this possible world, but since I might not have existed, there are possible worlds in which I do not exist), this is not the case for possible worlds themselves. Possible worlds exist 'outside' possible worlds.
Yes, via accessibility
If we want to say that there are possible worlds in which it false that there are possible worlds, we need different possible worlds to 'see' things differently. One way of doing this is to suggest that some possible worlds are not 'accessible' from other possible worlds. Then, for it to be the case that there are possible worlds in which it is false that there are possible worlds, we need for it to be the case that there is a possible world w, such that no other possible worlds are accessible from w.
Possible worlds and the semantics of modal logic
There is a close connection between possible worlds and modal logic – that is, the logic of words like 'possible', 'might', 'necessary' and so on. And the question of whether claims about the existence of possible worlds differ from world to world is closely related to questions about the logic governing words like 'necessary' and 'possible'. To give two examples:
It is quite plausible that, at every possible world, it is true that there is at least one possible world (i.e. at least one possible world is accessible), namely the actual (or rather, what that world thinks is the actual world). That is, every world is accessible from itself. This is closely related to a principle known as T, which says that, if it is necessary that p, then p. (Equivalently, if p, then it is possible that p.)
Suppose that we go with the 'no' answer - so that the set of possible worlds is the same at every possible world. Or, in terms of accessibility, every possible world is accessible from every other possible world. If this is the case, then, as well as the T principle, we get the principle that, if it is possible that it is necessary that p, then it is necessary that p. Some people think that this is plausible, some people think that it is not. (Here are a couple of papers on this issue: Staphanou (2000), Gregory (2001).)
There are many more such relationships (see this SEP article).