Pushing black and white film is very common. There's so much on the internets about shooting Tri-X at 1600 that I even pushed my first roll to 1600 without having tried it at box speed. Not many people talk about pushing slide film however.
After pushing Tri-X I tried pushing Portra. That didn't work as well as expected. You can push it but pushing will come with color shifts. It's possible to try to fix them in post, but it's not easy. C-41 in general is a very very standardized process. Any variation will lead to very ugly results.
When I processed C-41 and E-6 at home I actually found that E-6, with all it's steps, is easier. E-6 seems to be less temperature dependent than the C-41 process. When I messed up in E-6 I would get slight color casts that were either barely noticeable or easily corrected.
When I messed up in C-41 the results were hurting my eyes.
So on a trip to Los Angeles I took my two Olympus XA2 cameras with me. One always had Provia 400X and one always had Provia 100F loaded. I carried one in my hand and one in my backpack, using them depending on the light and time of day. Towards the last day I finished another roll of 100F and figured it wasn't worth reloading and decided to just use up the 400X loaded in the other one. My friend's mom, who was driving me to the airport, was nice enough to give me a small tour of Los Angeles and I ended up taking more photos than I expected. Long story short. It was a bright sunny day and I loaded another roll of 100F forgetting that this camera's meter was set to 400 speed from the previous roll. I shot the entire roll not noticing this until I rewound it. Back in Tokyo I dropped them all off to CREATE Lab in Shinjuku and just told them about the accident. They assured me that it's no problem pushing this film two stops. It cost me only 100 yen more to push it and I am very pleased with the result I got.
Realizing that this actually works I shot another roll pushed in Tokyo.
Knowing that slide film has a super tight exposure latitude compared to B/W or color negative film, I didn't expect it to push so well. With the discontinuation of Provia 400X this is great news. I have the freezer full of 400X, but when it runs out I know I can push 100F and get decent results. Maybe I should just reserve the 400X for shooting at 1600 then. What other color film can you shoot at that speed?! Natura, my favorite I guess... but slide film does give you different colors. So this stuff is special!
Tokyo is film paradise! I can get color negative developed in 45-60 mins at five labs within walking distance. For slide film they take overnight. There are 3-4 one hour slide film labs but they're two stops away on the train. Either way, it's still cheap here. 750 yen for a roll of slide film and 850 yen pushed. I cannot complain. Summer is around the corner and I'll push some more Provia. I hope I don't run out before that Ferrania stuff becomes available!