How to manage competing offers while interviewing (4 companies)

I'm in the process of interviewing with 4 companies (yes, it's chaos). Companies A, B and C, I'm through the process and awaiting decisions or at the very final stage. At Company D, which is my top choice, I have multiple interviews scheduled tomorrow, and there would be one final one beyond that if I make it through, presumably next week.

Today, I got an offer from Company A. It's not a very good offer and I'll almost certainly turn it down, regardless of what happens with all the other companies. But can I/should I still use it as leverage to get the others to move more quickly?

I guess in my ideal world, I would use the offer from Company A to get Companies B or C to make their offers, if applicable (I would likely accept either of these roles if Company D rejects me). And then I would take any offer from Company B or C to Company D in the hopes that they can speed up their decision.

My biggest concern is that I don't want to put myself out of the running with Company D by using Company A's offer, since I know I won't take it regardless. I also just worry about the competing timelines with all of this, because I know especially if I get an offer from B or C, I'm not going to have a lot of time to make my decision.

I realize this is a convoluted question but just wondering if anyone has advice? Most of the advice and my experience in the past has only ever involved two companies; rare has the situation been where all tlhe stars align and the timing lines up on so many at once.

Thanks for your help!

You're killing it!!!! I will draft you a longer answer but before I do, take a look at this thread which reminds me a teeny bit of your situation
im emotionally invested in your situation hahah but seriously how did it go!!!