There are several reasons to believe that dark matter is a particle. The most widely accepted alternative explanations for the different phenomena that led us to conjecture dark matter in the first place, can collectively be labeled "we don't understand gravity well enough".
But no matter what, the effects of dark matter are sort of "localized". The rotation curves of galaxies suggest that there's an "extra" pull from matter inside the galaxies. That is, either there's more matter than we can see, or the matter that we can see pulls more than we expect. The same can be said about the interpretation of the velocity dispersion of galaxies in clusters of galaxies, and of massive objects acting as gravitational lenses. Also, in order to explain how structure has the time to form before the Universe expanded too much, something must have made matter collapse faster than expected.
If these forces were applied from an "outside" agent, you would have to come up with a very special way for the forces to act. The forces we know of all depend on the distance between bodies, either increasing or decreasing with distance. But if an outside force were to explain e.g. galaxy rotation curves, it seems it would have to repeatedly "switch sign", i.e. alternate between attracting and repelling.
I should say that I don't really know much about multiverse theories, but for such a theory to explain the observables, it seems there would be the need for many extra add-ons and ad hoc-explanation. The theory of dark matter (and to some extend those of modified gravity, I suppose) offer the most simple explanation.
And we like simple explanations.