Okay. So if two large systems (large in a quantum sense) interact in isolation, the quantum wave function describing the system becomes the cross product of the matrices that describe the individual systems. The number of dimensions of the Hilbert space of the wave function becomes extremely large, extremely quickly. Now when you measure that system it “collapses” to a single eigenvalue. In the MWI, all of the eigenstates of the system are realized in different “worlds”. That is an enormous number of worlds because of the high dimensionality of the wave function. These different measurements can’t fit into one more dimension. Then don’t forget each of those now separate evolving systems becomes entangled with its environment, forming more cross products, more worlds at a massively exponential rate. The dimensionality of this evolving quantum state is enormous and will never fit in four spatial dimensions. And this is why I say you can’t locate every part of the universal wave function just by adding one more spatial dimension. It’s dimensionality is far higher than that. Otherwise these different parts of the wave function would interfere with one another, but they do not. By the way when I was first learning about QM this same idea occurred to me too, but this is the reason I subsequently dismissed it. Or one of the reasons. As for string theory’s dimensions, you’re quite wrong. The whole thing is perfectly coherent and precisely defined. Though far above my mathematical pay grade, and I don’t doubt yours too. Dimensions don’t have to be Euclidean, as GR shows. They can have all kinds of curvatures.