Would make Krakatoa look like a complete joke...hundreds or thousands of times more material ejected and explosive power. There hasn't been a caldera blast like Yellowstone, or remotely approaching Yellowstone, in recorded human history.
Read below the explosive force of Krakatoa. Your claim of hundreds of thousands of times more powerful than Krakatoa would mean the end of the world.
.............Krakatau erupted in 1883, in one of the largest eruptions in recent time. Krakatau is an island volcano along the Indonesian arc, between the much larger islands of Sumatra and Java (each of which has many volcanoes also along the arc). There is a very fine book about the Krakatau eruption by Tom Simkin and Richard Fiske, so if you really want to know about the eruption you should go to the nearest bookstore or library to find that.
Here are some highlights from their summary of effects:
1. The explosions were heard on Rodriguez Island, 4653 km distant across the Indian Ocean, and over 1/13th of the earth's surface.
2. Ash fell on Singapore 840 km to the N, Cocos (Keeling) Island 1155 km to the SW, and ships as far as 6076 km WNW. Darkness covered the Sunda Straits from 11 a.m. on the 27th until dawn the next day.
3. Giant waves reached heights of 40 m above sea level, devastating everything in their path and hurling ashore coral blocks weighing as much as 600 tons.
4. At least 36,417 people were killed, most by the giant sea waves, and 165 coastal villages were destroyed.
5. When the eruption ended only 1/3 of Krakatau, formerly 5x9 km, remained above sea level, and new islands of steaming pumice and ash lay to the north where the sea had been 36 m deep.
6. Every recording barograph in the world ducumented the passage of the airwave, some as many as 7 times as the wave bounced back and forth between the eruption site and its antipodes for 5 days after the explosion.
7. Tide gauges also recorded the sea wave's passage far from Krakatau. The wave "reached Aden in 12 hours, a distance of 3800 nautical miles, usually traversed by a good steamer in 12 days".
8. Blue and green suns were observed as fine ash and aerosol, erupted perhaps 50 km into the stratosphere, circled the equator in 13 days.
9. Theree months after the eruption these products had spread to higher latitudes causing such vivid red sunset afterglows that fire engines were called out in New York, Poughkeepsie, and New Haven to quench the apparent conflagration. Unusual sunsets continued for 3 years.
10. Rafts of floating pumice-locally thick enouth to support men, trees, and no doubt other biological passengers-crossed the indian Ocean in 10 months. Others reached Melanesia, and were still afloat two years after the eruption.
11. The volcanic dust veil that created such spectacular atmospheric effects also acted as a solar radiation filter, lowering global temperatures as much as 1.2 degree C in the year after the eruption. Temperatures did not return to normal until 1888.