To describe the kinds of things that could verify the Many Worlds Interpretation of physics I thought of this sample. I do not particularly think the sample will work, it is just the sort of thing I am thinking of. Remember, you get a candy bar online if you come of with a testable procedure!
a nested MWI co universe. To build a nested MWI universe place a fiber optic circle around a small radioactive sample. say the light takes 10 time units to travel the circle, while the predictable radioactivity generates an MWI electron every 2 time units. The fiber optic circle is in the lightcone of the radioactive material. Because the circle time is longer than the radioactive time, the composition of the generated universe is contingent on two quantum events simultaneously. That simultaneous contingency is a kind of nested universe.
2)layer these nested universes at a circle, where each others lightcone angles into its nearest neighbors lightcone. This lightcone overlap forms a toroidal nested universe
3)measure something at the core of the toroid, as well as the outside of the toroidal area. Then also measure something at the actual toroidal interior area.
4)if the core and outside have the same value, yet the toroid part has a different value, and the value ascends with time (as the toroid of nested universes diverge from our universe) Then it is possible the toroidal universe is different from out own.
the something being measured might be photons, electrons, phase, capacitance, magnetic field. I do not know what would be different, it is just that it should be different, and the difference should go up with time as the toroidal universe has different MWI divergences from out universe.
5) you might have a very very different approach, it should be physics testable though.
(ascii graphic of lightcone toroid)