So. There's a group of nutcases in my setting; they are an ages-old, all-powerful secret society, yadda yadda yadda, control massive amounts of the world behind the scenes, have agents everywhere of every ethnicity, religion (or pretending to be that religion), nationality, etc.
The thing is, however, that they're basically a cult of Hephaestus/Vulcan that worships volcanoes. Their goal is to cause a supervolcanic eruption. To do this, they're going for a multi-step process:
Drill 10 kilometers (it's possible) underground in the Phlegraean Fields to drill into the cap over the magma reservoir under the guise of attempting to monitor the state of the volcano. Advancements in ground-penetrating radar have made the detection of these reservoirs possible. This stage is basically "finding a filled and sealed soda bottle underground".
Set off a long, skinny (it's got to fit down the borehole) 1-gigaton multi-staged Tellar-Ulam device to "take the cork out", as it were - to negate the lithostatic pressure that has so far prevented a second eruption in the vein of the Campanian Ignimbrite eruption, which this group sees as an attempted but failed manifestation of their god. This stage is basically "digging down and blowing the cap off of the soda bottle with a firecracker".
Pump water into the large resultant salt dome cavity with repurposed hydraulic fracturing technology in order to destabilize the volcano. This stage is basically "drop a Mentos in the bottle for shits and giggles".
The actual end result of this is that the cult/conspiracy/thing miscalculated, and they accidentally cause a supervolcanic eruption across the entire Campanian volcanic superstructure, resulting in a semi-apocalyptic event and a multi-year-long nuclear winter across the entire planet.
Now, I recognize that, provided that you portray things believably enough, willing suspension of disbelief is easy for the reader, but I'd also like this to be somehow grounded in some kind of realism. So, first question, out of many I have about this scenario:
Is it even possible (hypothetically, of course) to make a supervolcano erupt by nuking its top off and then pumping water into it?