This depends on the structure of the multiverse. In case of quantum mechanics it is possible, at least in principle, to come up with an experimental proof that a Many-World's multiverse exists. The following thought experiment has been devised by David Deutsch. Here one considers measuring the outcome of an experiment where two possible outcomes exist due to the measured system being in a superposition of the two states corresponding to a definite measurement outcome. According to the Many World's Interpretation (MWI), if one of the two outcomes is actually measured, the other possible outcome is also realized in a parallel World.
To prove that this other outcome really exists, one can consider performing the measurement inside a completely isolated system. If indeed the two possible outcomes really exist, then the entire system can be evolved back to the initial state. But, of course, that would erase the memory of the observer and so the observer wouldn't know that any measurement has actually been carried out. However, instead of evolving the state back to the initial state, it is also possible to let it evolve to a state where the measurement outcome is erased but the record of the fact that a measurement was actually made is kept. In principle, all possible so-called unitary transforms can be realized as time evolutions, and erasing the outcome while keeping the record that a measurement was carried out, is a unitary transform.
Now, if the state of the system had collapsed into a single state corresponding to the observer having observed one definite outcome, then carrying out the above transform will have changed the state of the measured system, while in the MWI it will yield the original state. The observer can then do additional measurements on the system to see if the state is the same, this requires repeating the experiment a few times and then carrying out an additional measurement to see if the probabilities match up with what one would expect if the state of the measured system is unchanged.