Ooo I have one! Hatoful Boyfriend! It starts out as a silly parody of dating games, where you, a human girl, date pigeons (represented with literal photos of pigeons), treated though they were the same pretty anime boys of any otome, but as you go you uncover strange clues that something isn't right, and a new path where there are DEFINITELY NO EMOTIONAL BREAKDOWNS OR GRISLY MURDERS IN THIS FUNNY BIRD GAME!!! by the end, it is a completely different kind of game that destroyed my heart!! But it's so strange and interesting, I really have a soft spot for it. I think it did a good job of a tone shift that was a big surprise, but because of how it was foreshadowed and hinted at, it doesn't feel random.
THAT SAID, THO, I usually actually prefer to get what it says on the tin. xD I have a very specific and narrow ability to handle emotional distress in my fiction, so shows like Steven Universe that start out fun and quirky and then delve into deep and real emotions can often be too much for me -- if it's a contained thing like a movie or game it'll just be a powerful experience, but if it's a comic or a show that you come back to over and over, I might nope out after a season when things start getting too real and stay there.
I'd say that in my own work, I shoot for scenes and moments to hit different notes rather than the overall story having a tone shift. I think my story is the kind of story that it appears to be from the start (a friend of mine described the tone of my work as "Fantasy Voltron" and I love this) -- there are moments that lean silly, and there are moments that lean emotional, but it doesn't really take a turn in one direction or the other. At least, that's what I'm going for! I guess we'll see!!