"Runs up flagpole" is an idiomatic expression that means to propose an idea or suggestion for consideration or approval. There are several synonyms for this phrase, such as "floats an idea," "presents a proposal," "offers a suggestion," "puts forth a notion," or "suggests a concept." These phrases all convey the same idea of introducing an idea for review or discussion. It is important to use these synonyms appropriately in different contexts to convey the intended meaning. When communicating in professional settings, choosing the right phrase can enhance clarity and effectively communicate your message to your audience.