Often times, when authors write themselves into corners and feel like they want to continue telling their story without breaking the logic of the narrative. This often proves to be an impossible task, especially if not planned out beforehand, however some authors manage to take advantage of gaps in the narrative well enough that a sequel/continuation actually makes perfect sense. 

1. Dragon Ball Z - Perhaps the most legendary example of this trope, Dragon Ball Z takes a comedy focused martial arts Manga steeped in asian mysticism and gag comedy and turns it into the preginator of modern shonen battle Manga focused primarily on fighting alien threats with the power to destroy worlds. The reason this twist works well enough despite using many hated tropes (Hidden Brother, Introducing aliens into a story that wasnt about that) is because Dragon Ball is silly enough that Goku being an alien the entire time isnt actually that far out there when it comes to tone and suspension of disbelief in Dragon Ball's greater story. Gokus origins had always been a mystery asking to be solved, and for it to be solved in such a way that the entire cast is being dragged into a longer story actually works very well, as DBZ is pretty much just a continous series of consequences and solutions that stem from raditz's arrival. The main reason why this works is the gradual shifting of tone throughout original Dragon Ball, as it was always slowly progressing to a more serious (if still silly) tone from before the big twists even came. 

2. Jujutsu Kaisen Modulo - Following in much the same vein as Dragon Ball Z, jujutsu kaisen's sequel sets up a 70 year time skip and the arrival of potentially hostile aliens with futuristic technology that coincidentally have the same powers as the protagonists of the story. Either of these tropes would be enough to ruin a story if not handled properly, but Jujutsu Kaisen actually flourishes in this context and delivers the narrative very well. For one, this context isnt that different from what JJK was doing before, the original series introduced threats from the past, the natural inverse of this is to introduce threats from the future, and while JJK's simurians arent time travelers they represent a futurism absent from original Jujutsu kaisen. 

The main reason jt works is because this twist is meant to reinforce the main themes of the original story, while also introducing new ideas. JJK's main narrative beats center themselves around power structures, and how they effect the people beholden to them and the people in charge of them. In order to keep this narrative going after the main series has already concluded, it only makes sense to introduce forgein, maybe even alien power struggles into the story.

3- Percy Jackson into Riordanverse - Rick Riordan's mythology series starts out as a modernization of many Greek Mythological ideas in the context of an adventure centered around titular character Percy Jackson. Percy Jackson goes on 5 adventures across 5 books, ends a war between Chronos and Olympus, and goes home to camp half blood. A satisfying ending by all accounts, but Riordan wanted to continue this mythological series without feeling like he was cheapening Percy 's story. His answer: write completely disconnected mythological stories centered around different mythologies. Normally,  stories centered around mythology only focus on one, as most people assume multiple pantheon existing together cant make sense as there can only be one mythology, one series of gods at the center of any given story. Riordan challenges this by merging Greek and Roman mythology into the same continuity with the heroes of Olympus series, focusing on a parallel roman camp of demigods perpendicular to the original camp halfblood. This twist works so well because in reality, Greek and Roman Mythology isnt that different, The roman and Greek gods are aware of each other because, well, they are each other just with differing cultural attitudes. 

Lost Hero (the first book in Heroes of Olympus) in specific works so well because its such a flashbang picking up from the Last Titan (The last book in Percys series) as it picks up with completely new characters in a completely new setting with completely new gods that feel extremely familiar but arent and cant be the same ones. The reality of the situation slowly unfolds across the Heroes of Olympus books in a way that feels very well written (although at times convinent)

4. God of War- The original God of War trilogy ends off on a bleak note, Kratos, achieving his revenge he sought after in the very first game, finds himself with nothing. A destroyed world and no will to live, Kratos falls into the water and isnt seen again. God of War 4 picks up in an unfamiliar environment, with our only familiar face being a much different looking and feeling Kratos. In the games opening act, it is revealed slowly through subtext Kratos has found himself in the world of Norse Mythology, and founded himself a family that hes fighting to keep a hold of.

 Introducing a completely new world in a story focused on a completely contrasting mythology works very well from a narrative perspective. Kratos' world has literally fallen apart and he needs to start over completely if he even wants to at all. Its never said explicitly, but Kratos' is implied through subtext to have been destitute until he happened to stumble into the Norse world and onto Freya, who renewed his will to live through their love for each other.

[Meta Trope] The sequel shouldn't make sense but it does anyway