You can only get what you ask for, in general, with luxury properties that don't have official frequent guest/loyalty programs. If you don't ask for more, you rarely will get much more.
If you want to use a Virtuoso agent, that can be helpful, but rarely more than a category or two upgrade in my (admittedly limited) experience.
I almost always get upgraded...but then I always ask. As much as possible, I travel at shoulder season or low season when occupancy is lower and upgrade chances are higher. When you ask for an upgrade and there are few guests, it's a lot easier to get a big upgrade. I never travel at high season if I can avoid it....and then I rarely expect any upgrade.
I almost always reach out to the GM or comparable person to ask for a specific upgrade. Even if I don't get what I want, I often find myself upgraded to something a lot nicer than I otherwise might.
For some properties, I do negotiate. If you don't want to negotiate, don't expect the amazing upgrade to fall in your lap.
For some properties, I simply reserve the amazing suite that I want. Sometimes I negotiate a better price; sometimes I accept the given price.