To reveal information to the audience that the characters on stage don't know. A split stage can be used to reveal information to the audience that the characters on stage don't know. For example, one scene might show a character making a plan, while the other scene shows the person who they are planning to deceive.
To create a sense of contrast or irony. A split stage can be used to create a sense of contrast or irony. For example, one scene might show a character living a life of luxury, while the other scene shows a character living in poverty.
To add visual interest to a production. A split stage can be used to add visual interest to a production. For example, one scene might be set in a brightly lit room, while the other scene is set in a dark and shadowy room.
To focus the audience's attention on a particular character or object. A split stage can be used to focus the audience's attention on a particular character or object. For example, one scene might show a character giving a speech, while the other scene shows the audience's reaction to the speech.