On the subject of suturing distinct systems together: Some DMs are up for doing so, but it's pretty rare, especially if you're actually looking at proper cross-edition integration. If it's technically "within" one edition, the odds go up, but not by a lot.
I say this because 3e produced a lot of third-party content and a metric butt-ton of homebrew, and innately has a little bit of "cross-edition integration" with some of its own content. Because, you see, there were books published for 3e that were never updated for 3.5e, which technically makes the 3e book the "definitive" book...except that much of that stuff is riddled with holes. The big stand-out here is Savage Species, which has some pretty cool stuff in it, but some of it reflects the even-more-broken nature of 3.0 vs 3.5. There's also sometimes interest in books that did get replaced with versions that folks consider inferior, like the psionics handbook.
As an example of the "within" edition game-surgery I've seen, I've played in games where:
Base system was PF1e, but wildshape is done by 3.5e rules, and you could import any content from 3.5e with DM approval (and 99% of the time it would get approved)
Base system was 3.5e, but 3.0 content was approved on a case by case basis (often required tweaks/alterations), and PF content could be converted if you asked very nicely and it passed a smell test for stinky cheese
Base system was PF1e, except that all characters had to take Spheres of Magic spellcasting instead of default, and some other 3PP content was available
Base system was...I guess theoretically PF1e, but literally all (and I mean literally, genuinely all) content from 3.0, 3.5e, PF1e, and ANYTHING published on the online Pathfinder stuff could be used, so long as the DM looked over it first. By far the most gonzo game I've ever seen, with PF's version of epic boons and a baseline of "tri-stalt" with a side of "feat-stalt" and.....yeah. It was nuts.
So, within the incredibly byzantine and extensive library of "stuff that can be seen as in some way belonging to 3rd edition D&D," such game-suturing is...not necessarily common, but a hell of a lot more common than any other form of game-suturing. Because usually, if you're going to be trying to staple two+ genuinely different systems together, it's often easier to either (a) actually use just one system, but create extensive homebrew inspired by the other system(s), or (b) actually use a third system that is capable of relatively conveniently expressing the other systems' contents without massive overhauls.