Successful sequels require strong characters and a significant change in setting & plot to differentiate the sequel from the original.
This is a necessity because the new story must stand on its own. This is where Hollywood falls on its face with sequels.
Prime example: Heinlein's Starship Troopers is a favorite science fiction novel and was made into a feature film in 1997. As a film, it was very successful and made quite a lot of scratch.
Since Hollywood bought the rights, they decided to cash in on the franchise. They hired some writers and a whole new cast and did Starship Troopers II: Hero of the Federation which sucked raw balls.
Not to be outdone they did Starship Troopers III: Marauder which still sucked balls but was not quite as bad as SST II.
Heinlein only wrote the original story. Everything else was ripped off from his original ideas and regurgitated (as cheaply as possible) to cash in on the rights.
The point is that simply because you CAN do a sequel doesn't mean that you should.
Ask yourself:
Is it contrived? Does the story flow naturally or is it a reach? [this is where Hollywood falls on its ass]
Are you trying to clone a hit? Ask Hollywood- it can only rarely be done and usually fails.
Did you plan a series or sequel to start with? Did you leave room and open questions from the first story?
Are the characters and setting strong enough to support a continuing story line? Often Hollywood does low-budget sequels with a new cast and invariably screws up any possibility of the sequel succeeding.
Can you be consistent in the new storyline? If the original story was a coming of age story, is the character a young adult in the sequel? Does he/she use the lessons learned in the first story line? Did they grow? Is that growth consistent?