The shuffle
library routine lets you provide a source of random numbers (if you don't, it'll use the built-in default). So, in theory, if you have a better source of random numbers - maybe, something connected to a Geiger counter or a "white noise" radio station, or something getting numbers from random.org - you could use that instead. Probably more useful, if you're testing, you could connect a source that returns the same sequence of numbers, which would make sure your test case is repeatable and always generates the same shuffle every time.
You could, in theory, develop a random number routine that will allow you to control exactly how much shuffling the shuffle does; but that means you need to know exactly how shuffle
works and exactly what numbers you'd have to return to "guide" your results to where they want to go. In theory... it's not too difficult, the algorithm used is very well-documented (Fisher-Yates), and during the call it generates n-1
random numbers, the first to select an element from index 0 to n-1, to swap with the last element, the second to select an element from 0 to index n-2, to swap with the last-but-one element, and so on. So yes, you could use this to control the shuffle, like @JohanLundberg example which forces the shuffle to shift - but it would be very hard to use that to control the shuffle (since each iteration, all the original data is jumping around).
Short answer, if you need specific constraints on a shuffle, such as "only swap neighboring elements" - you'll be better off implementing your own, perhaps using the shuffle source code as a guide.