Dream up is a common phrasal verb that means to create or think of something new or unusual. There are many synonyms for this phrase that can be used in different contexts. Some of these synonyms include "brainstorm," "conceive," "imagine," "invent," "contrive," "originate," "devise," "formulate," "incubate," and "fancy." Each of these words has a slightly different connotation, but they all involve the act of creating or imagining something new in one's mind. Whether you're writing a story, designing a product, or simply daydreaming, there are many ways to express the idea of dreaming up something unique and exciting.