Video game sequel

What's the best video game sequel of all time? What made it so great?

Now my mind is racing analyzing this.

What makes best sequel? Is it the best ever game that is a sequel or best as sequel? A sequel that most improves from the previous game(s) or a sequel to a great game that's able to match it? And do you count parts of loose series like Final Fantasy or only direct sequels?

Let's see what kind of candidates I can think of...

Phantasy Star IV: after the less popular, experimental PS III came a grande finale for the (original) Phantasy Star series. PS IV beautifully combines elements from the first three very loosely connected games in story, graphic style and gameplay while still throwing in something of its own. If not the best sequel of all, I'd say this is certainly best series finale I've played.

Dune II: taking only part of the strategy element of the first game (more directly based on movie/book), the second Dune game basically created the whole RTS genre

TIE Fighter: a great sequel to a good game, both similar and different enough, improving in pretty much everything

King's Quest IV, Larry 3: following IMO worst parts of their series, not only return to good form but in some ways peak of whole franchise

Privateer 2: I call it "the best movie I've ever played"; not actual sequel to the first game, but same concept executed even better, open world freelancer space game with pretty unique combat/weapons

Max Payne 2, Carmageddon 2, Monkey Island 2, Populous II, Master of Orion II, Wing Commander II: sequels to some of greatest games ever that are very similar and almost as good as the first, in some aspects even better