Dream-up meaning

To have an imaginative, unusual or foolish idea, to invent something unreal.

It's as if he were giving a performance of some character he's dreamed up, and his pale eyes wander in search of effect even in his apparently wildest moments. - Steven H. Gale: Encyclopedia of British Humorists.

Since he had no way of returning to his homeland, and since remembering it made him suffer, he dreamed up a homeland he'd never had... - Fernando Pessoa, Richard Zenith: The Selected Prose of Fernando Pessoa.

I am not arguing that I can dream up any reality I like. - John Louis Lucaites, Celeste Michelle Condit, Sally Caudill: Contemporary Rhetorical Theory.