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.