Digital sensors have come a long way in the past 15 years or so, but even so, pushing a shot four stops is getting close to the limit of file latitude in most situations. So, how well can film hold up when you do the same? The answer is very well.
If you don't know Kodak Tri-X, it's by far one of the most ubiquitous stocks out there, and if you're interested in trying out film, I highly recommend grabbing a few rolls, especially because it's remarkably forgiving of any exposure miscues, making it perfect for beginners looking to get their feet wet. In this video, Vincent Moschetti push-develops a roll of Tri-X four stops, increasing its effective rating from ISO 400 to ISO 6,400. Pushing Tri-X (and other stocks) a couple stops was actually a very common practice back in the day, particularly among sports photographers and photojournalists, but it's especially interesting to see how the results stack up in an age when we're used to digital sensors and the near-remarkable results we can get out of them. Personally, I think the Tri-X did quite well, and I find the grain much more pleasing than digital noise.