Nonlinearities in quantum mechanics? Linearity is what makes quantum mechanics amplitude-independent. If you ruin that, then the laws of nature will change from moment to moment as the wavefunction moves to fill more and more of Fock space. Suffice it to say, QM's leading order is 1, and any higher powers are way out of reach.
Unless, that is, worlds are top-level entities in your physical theory somehow, which then brings in the full weight of the 'what does it have to do, kill a puppy' rant against it.
Speculation is important for forecasting; it's also fun. Speculation is usually conveyed in two forms: in the form of an argument, or encapsulated in fiction; each has their advantages, but both tend to be time-consuming. Presenting speculation in the form of an argument involves researching relevant background and formulating logical arguments. Presenting speculation in the form of fiction requires world-building and storytelling skills, but it can quickly give the reader an impression of the "big picture" implications of the speculation; this can be more effective at establishing the "emotional plausibility" of the speculation.
I suggest a storytelling medium which can combine attributes of both arguments and fiction, but requires less work than either. That is the "wikipedia article from the future." Fiction written by inexperienced sci-fi writers tends to generate into a speculative encyclopedia anyways--why not just admit that you want to write an encyclopedia in the first place? Post your "Wikipedia articles from the future" below.