base something on something
base something upon something

But his was all based on the woman she had once been.

All of them are based on real life in some form or another.

But she's based on the other side of the world.

The film is based on the play of the same name.

The games are based on the book of the same name.

The series is based on the 2004 film of the same name.

Based on the evidence so far, how would you answer those questions and why?

The park was based on the book rather than the film.

The next question would be based on the answer to the first.

The show was based on the board game of the same name.