If it is true that all possible outcomes actually happen in at least one of the many-worlds, then a global quantum suicide machine (such as the one that's just about to be activated under the Franco-Swiss border) could be used as a veritable genie.
All possible outcomes happen if everything that happens or doesn't happen is determined at some point by a quantum event. If this is true, then the operators of the global quantum suicide machine can say "We'll activate it today if we don't win the lottery today." Then, only two types of world will exist: Those in which the experimenters all won the lottery, and those where the quantum suicide machine broke down (in which case, the experimenters can try again). From the point of view of the experimenters (and the rest of the world, too), it will seem like there's a certain probability of either their wish coming true before they hit the button, or the machine breaking down, every time they even consider pushing the button. For those outcomes that are less improbable than the machine breaking down, the experimenters would tend to get what they wanted. For other outcomes, the experimenters could try several times.
If they can increase the reliability of the machine arbitrarily, then they can also increase the improbability of their wishes, along with the probability of their wishes coming true when they ask. For example, they could activate the machine only if a meteor shower doesn't etch their names on the Moon.
If the wish can't be influenced by one or more quantum events, then the only worlds that would exist would be those in which the machine broke down.
There's no telling how far the experimenters would be able to go. Is anything truly impossible, or are some things merely ludicrously improbable? Is there anything the experimenters could ask for but never get?