This is an actual testable prediction. Suppose such an exception is found experimentally (for example, self-decoherence due to gravitational time dilation, as proposed by Penrose, limiting the quantum effects to a few micrograms or so). Would you expect EY to retract his Bayesian-simplest model in this case, or "adjust" it to match the new data? Honestly, what do you think is likely to happen?

Honestly, when the first experiment shows that we don't see quantum effects at some larger scale when it is otherwise believed that they should show up, I expect EY to weaken, but not reverse, his view that MWI is probably correct - expecting that there is an error in the experiment. When it has been repeated, and variations have shown similar results, I expect him to drop MWI, because it now longer explains the data. I don't have a specific prediction regarding just how many experiments it would take; this probably depends on several factors, including the nature and details of the experiments themselves.

This is from my personal model of EY, who seems relatively willing to say "Oops!" provided he has some convincing evidence he can point to; this model is derived solely from what I've read here, and so I don't ascribe it hugely high confidence, but that's my best guess.