There are many multiverse theories and they can all be tested.
Many Worlds: The theory that there are no real "probability waves" in QM, merely overlapping realities that diverge at the time the "waveform" collapses.
This is an easy one. Entangled particles operate using the same physics as wormholes. If one of the entangled pair is accelerated to relativistic velocities, say in a particle accelerator, they will not exist in the same relative timeframe. It would seem to follow that if Many Worlds is correct, one of the particles will be entangled with multiple instances of the other particle, which would imply that every state would be seen at the same time. If the options are left spin and right spin, you'd see an aggregate state of no spin even if no spin isn't a physical possibility. And seeing something that doesn't exist either means you're in a Phineas and Ferb cartoon or Many Worlds is correct.
Foam Universe: This is the sort described in the article.
Yes, impact studies are possible, but they're only meaningful if you have enough data and you can't possibly know if you do. You're better off trying to make a universe, preferably a very small one with a quantum black hole at the throat of the bridge linking this universe to that one. What you will observe is energy apparently vanishing, not existing in any form - mass included, then reappearing as the bridge completely collapses.
Orange Slice Universe: This conjectures that multiple, semi-independent, universes formed out of the same big bang and will eventually converge in a big crunch.
It doesn't matter that this universe would expand forever, left to its own devices, because the total mass is the total mass of all the slices. Although they are semi-independent, they interact at the universe-to-universe level. In this scheme, because there's a single entity (albeit partitioned), leptons cannot have just any of the theoretical states. The state space must also be partitioned. Ergo, if you can't create a state for an electron (for example) that it should be able to take, this type of multiverse must exist.
Membrane-based Universe: This postulates that universes are at an interface between a membrane and something else, such as another membrane.
However, membranes intersecting with the universe are supposed to be how leptons are formed, in this theory. The intersection will be governed by the topology of the membranes involved (including the one the universe resides on), which means that lepton behaviour must vary from locality to locality, since the nature of the intersections cannot vary such as to perfectly mirror variations in the shape of the membrane the universe is on. Therefore, all you need to do is demonstrate a result that is perfectly repeatable anywhere on Earth but not, say, at the edge of the solar system.