I'm struggling to think of many games that switch genres at all, tbh. I applaud any devs who make the effort though.
Viewing post in A game I'd like to see.
Depends on what constitutes a genre.
The "genre" list on itch reads
Action, Adventure, Card Game, Educational, Fighting, Interactive Fiction, Platformer, Puzzle, Racing, Rhythm, Role Playing, Shooter, Simulation, Sports, Strategy, Survival, Visual Novel
And if we want to have a switch in genres, or a mix up or containing several of those.
Most games that feature minigames might qualify.
I believe many have one genre on top of another. Like a shooter engine featuring puzzles. Prime example is Portal. That one even "changes" genres, depending on if you jump into the fire or not after the puzzles.
I am missing management and sandbox in that list. Sport games often have a manager aspect. You might play the sport events, but also have the management of your team. But I do not think this counts as changing genres, as it is meant to have both aspects simultanous.
If we wanna count them, many clicker/idle games somewhat change. They have a start phase that might count as action and then become something akin to optimisation strategy with so little action that you can literally idle or even offline play them.
Well there are old games I recall which has multiple genres in it. The best example I could give is Battletoads. I haven't played arcade version nor the newest one but the Genesis and SNES have different genre in each stage.
There's also Actraiser, which is primarily hack n slash platformer but it has management or strategy genre/mode in it.