As this is the ever-highly speculative Science board, I put to you a highly speculative scenario: Are you a bad enough dude/construction company/government agency/super villain to stop a volcano? Can you think of a way to take enough energy out of the equation to make a volcano sputter rather than explode?
I say this with the threat of Uturuncu popping its top sometime soon and potentially messing with the weather even worse than Pinatubo did. Also, I'm all about job creation...
Don't hold back! I want to hear crazy ideas.
Ok, I'm thinking our best bet would be >>15-san's idea.
According to Wikipedia, the Altiplano-Puna Magma Body has a volume of 50,000 km^3. Our goal should to change the melt from felsic/intermediate to mafic. This requires increasing the temperature by ~300 C, and the iron composition by about 7%.
Using a density of 2.5 g/cm^3 for andesite, and a specific heat capacity of 591 J/kg*K, we get 1.25*10^17 kg of magma, containing about 9.5*10^22 J of heat energy. Increasing the temperature by 300 C would require an additional 4*10^22 J. For reference the largest nuke ever set of (Tsar Bomba), released 50,000 tons of TNT worth of energy, or about 2*10^14 J. We'll need about 200,000,000 Tsar Bombas to pull this off. I didn't look in to it too far, but there is probably enough uranium on the planet to make these bombs.
Next is the iron. Probably the easiest way to do this is to drill grid of boreholes (like >>7-san mentioned) across the Altiplano-Puna plateau, and just feed the drill steel straight into the magma. To increase the iron by 7%, we'll need 2,000 km^3 of iron, or 1.4*10^16 kg. World pig iron production was 1180 million metric tons in 2015, so we'll only need 12 years to produce that much.
In short, it is a lot more feasible than you might think. Obviously, I haven't considered the logistics of getting everything to the mountain. Also, I don't really know how we would get the nukes to the magma. More boreholes?
Finally, the price. As I write this the price of pig iron is $400 per metric ton, and uranium is $30 per lb. Ballpark, this gives me 5 quadrillion USD (5*10^15) for the raw materials. The job market looks good too. We'll be employing most of the planet's population for upward of a decade.
Some additional thoughts:
The nearest town is Antofagasta, which already has a big port due to the mining companies. Also, about half of the distance to the mountain is already covered by Ferrocarril de Antofagasta a Bolivia. We would likely have to lay ~200 km of new rail from Calama to the mountain.
Additionally, the current railway only handles about 2 million tons of freight per year, so it would need to be significantly expanded. The Daqin railway in China can transport 440 million metric tons per year, so three lines similar to that would be sufficient.
The port will need to be expanded, as well. Ningbo-Zhoushan port, also in China, supposedly the largest port in the world by tonnage, would almost be able to handle the load. I couldn't find how many berths are in Antofagasta, but we will likely need about 200.
Finally, I think that producing the uranium for the nukes will probably require the most effort. Refining an entire planet's worth of uranium is a non-trivial task. According to Wikipedia, it takes 62 SWU to produce 10 kg of low-enriched uranium. If current world enrichment capacity is 66700 SWU/yr, we will need at least 100,000 times more enrichment capacity to hit our 12 year schedule. (Someone should double check this calculation.)
Also, I just realized I screwed up my calculation for the Tsar Bomba. One detonation actually produces 2*10^17 J, so we would only need 200,000 bombs.