Okay, let's start with a "typical" ceiling consisting of one sheet of 1/2" drywall directly screwed or nailed into the joists. That's our baseline.
Let's now replace that 1/2" drywall with 5/8" Type X drywall. Net loss is 1/8" and it gives us marginally better soundproofing.
Let's add another sheet of 5/8" Type X drywall. Now we have Joist + 5/8" DW + 5/8" DW, giving us a net loss of 3/4". The soundproofing is now notably better than the baseline.
Why not add a layer of Green Glue in between the drywall? The thickness of the material shouldn't change in any easily measurable way (save using a micrometer) but the sound reduction will be noticeably better than even the standard double layer.
But now we'll kick it up a notch and decouple, in addition to adding mass. This is where the true bang for the buck kicks in.
The least amount of lost vertical space would be to create floating joists between your existing ones -- but this does assume that you also have floating walls (a "room within a room" construction method). You'll lose around 9" in each dimension for width and length of the room. In theory, you could create your new joists and new walls to be maybe 1/8" below your existing joists. That would give you a net loss of 7/8". That would assume some pretty straight existing joists, though, and that's not been my experience. It's probably safer to assume around 1/4" clearance, which creates a net loss of 1". This will be your close-to-ultimate soundproofing solution (and not just for the ceiling).
You could get a similar amount of lost vertical space by offsetting clips and channels into the existing joists using blocking. See this illustration from the Soundproofing Company:
This gives you roughly identical vertical loss as the floating joist solution. It has very similar soundproofing capabilities to the floating joist solution, albeit costing a bit more and not addressing the walls or flanking.
If all that seems to finicky, then the standard solution is to use 7/8" clips and channels with the two layers of 5/8" Type X drywall (and Green Glue). Net loss there is 1-5/8". It has the same excellent soundproofing abilities as the "blocking" solution, but far easier to install and only giving up a maximum of 5/8" more.