Screwed by the Lawyers: Disney ended up limiting the appearances of King Louie when the widow and family of Louis Prima, the voice of Louie in the original film, sued them over the stunning similarities of Prima's voice when Jim Cummings voiced Louie in TaleSpin. This resulted in Disney writing him out of the sequel, replacing him with an Expy named King Larry in House of Mouse, and have any appearance of him reduced to complete silence.
Before that, the film was a closer and much darker adaptation of the book.
According to Amy Mebberson, one of the animators for Jungle Book 2, there were ideas for a third Jungle Book. One idea was about Baloo and Shere Khan getting captured by hunters and sent a Russian circus, Mowgli and Shanti going after them to save Baloo, and Shere Khan possibly getting over his desire to kill Mowgli through the course of the film.
Long before The Jungle Book 2, development for a sequel had already been planned in 1968. It was initially pitched as a record story (entitled More Jungle Book) however it was rejected as an animation out of respect for Walt's dislike of sequels. The record featured original tunes provided by Phil Harris and Louis Prima (who reprised their roles as Baloo and Louie respectively), a snippet of which can be found here.
Trivia from The Jungle Book (1994 live-action movie):