If there's no room for improvement, it should maintain the quality. Difficulty wise, it should be on par with the original, and in terms of genre, it depends. If it's a gradual change over several games, sure. I don't want my FPS turning into a 4X overnight. Most importantly, it should continue the story.

Mass Effect is a good example, the gameplay changes were gradual. It went from an RPG with shooter elements to a shooter with RPG elements. Story wise, they continued it well (the fiasco at the end doesn't count) and the consistently improved on everything in the game, from inventory management to cover mechanics.

I think for more story orientated games, you can either go bigger, better, and more badass; or go in the more subdued direction Majoras Mask did, which is pretty much the perfect execution of a sequel.

It maintains all the core elements of the first game, while at the same time evolving them and revealing them to be part of a larger more meta and philosophical structure. It focuses on the ramifications of the hero's decision in the first game, and directs all it's themes towards expressing his decline into madness. A familiar yet freshly strange continuation of the story, which is more character focused that the previous.

You could also just try to make the same game again, but I think this is actually the most mediocre of approaches. Freshness of the concept and motivation to design it will have faded and it is just going to lead to something less interesting than the original no matter what you do. This is more along the nature of Twilight Princess as a sequel, and although it was an aesthetically pleasing title with some good elements, it's ultimately still in it's predecessor's shadow.