Can entanglements themselves be entangled? In other words, could there be higher dimensional entanglements between entanglements? For instance, this could allow us to entangle two entangled-far-away pairs to create a system of four entangled particles.
I am sorry if this sounds like a silly question.
 A: Entanglement is a property, so it doesn't make sense to "entangle entanglements". However you can entangle entangled objects. And indeed, if you have two entangled pairs, you can create four-particle entanglement that way. For example, you could create a four-particle cluster state (cluster states are special entangled states useful for quantum computing) by taking two Bell pairs, and do an entangling operation between one of the particles of each pair.
Note however that you still need to bring those particles together. You don't need to bring all the particles together, however; in my example above, the second electron of the two Bell pairs could be both far away, and yet they'd still be part of the four-particle entangled state.
You can even "measure out" the entanglement from the two particles you did the entanglement operations on, and end up with the two other particles forming an entangled Bell pair despite them never having been close to each other. That basically is what happens in entanglement swapping (except that instead of first entangling and then "measuring out" you do an entangling measurement, but as far as the remote particles are concerned, that's equivalent).
However note that you cannot use that to entangle previously unentangled particles. While in the entanglement swapping case, the two particles that get entangled need never have come close to each other, they both already have been entangled with another particle each, and those "entanglement partners" indeed did come close to each other.
Especially if you have two entangled pairs which are in different places, there's no way to entangle them without either getting at least one of the particles of each pair together, or using a third entangled system where one pair directly interacts with one part of that third system, and the other pair directly interacts with the other part.
So entanglement can only be created locally, but it can be "redistributed" along existing "entanglement connections".
