Oh Banjo Tooie was amazing! I loved Witchy World, made sure to get burgers and fries.Banjo-Tooie and Pokémon Gold/Silver I’d say are top tier sequels. Smash Bros. Melee as well was a huge leap I wasn’t prepared for either. Paper Mario 2 and Halo 2, also very good. Red Dead Redemption 2? technically a prequel, but still, massive improvement.
Unfortunately some of my favorites, a bit more debatable whether they’ve improved on anything but I still enjoy them as follow ups. No More Heroes 2 had some unfortunate tradeoffs, Deadly Premonition 2 felt it had even less of a budget sadly but the story concluded very well. Deus Ex: Mankind Divided was a game I enjoyed a lot given MGSV ditched a ton of good stealth mechanics - the only problem being Square cut it short.
Oh Donkey Kong Country 2: Diddy Kong’s Quest was incredible! Loved that game!Some of these have been mentioned already but I can't just not mention them too:
Donkey Kong Country 2, Metroid Prime 2, Banjo-Tooie, Majora's mask, Monkey Island 2, Turrican 2, Timesplitters 2, Perfect Dark...I'll stop it here because there's technically tons of games that could qualify for this list.