Alastair Reynolds in Chasm City has aliens that, from memory, manipulate the Higgs field and do quite weird things. They are not from another "dimension" though, just using this as tech.
Dimension is a bad word here from what you are talking about, I think you mean "other universe" in your musings. This is because one could easily imagine that a universe like ours but has four or more 'open' dimensions that would quite happily exist with our basic three dimensional part of it, as actually there have been a number of theories that use multiple dimensions that make up our universe. In some versions of M-theory they posit that our 3-D universe is interaction of two higher dimensional branes, and other theories speculate that gravity is special and 'weaker' than the other forces because it can leak into other dimensions that we can't currently observe.
Thus why not have other matter that can freely use all four (or more!), instead of being constrained to the three we use? In this case this more general matter, which is happy to live in our universe everywhere could quite easily 'hide' from us as there would be an infinite amount of space for this 4D+ matter (and aliens made from such matter) to live in, only occasionally popping into existence to us 'flatlanders'. A four dimensional object - even one that was just dumb matter - would behave amazingly to us 3-D'ers. It could pop in and out of existence, appearing substantial one minute, then alter shape in a snap in ways that we would deem impossible.
Could it also be that the constants and laws of nature are a result of our 3-D universe interacting with this bigger multi-dimensional space? And that physics in the higher dimensions could make it possible to alter our more limited 3-D physics by altering something close to our feeble plane?
Maybe such events do leave a mark? (I'm looking at you Cosmic Microwave Background cold spot.)
You don't necessarily need to invoke destruction of space and matter in these models either, so spotting such intrusions would be difficult.
Anyway pure speculation. Keeping it SF, I do remember Greg Bear writing a couple of nice stories about 4D aliens.