The phrase "be out for" is commonly used to indicate the intention or purpose of someone's actions. It's often associated with negative or harmful behavior, such as being out for revenge, or being out for blood. However, there are many synonyms that can be used in its place to convey similar meanings. These include "on the hunt for," "seeking," "pursuing," "looking for," "aiming at," "targeting," "searching for," "vying for," and "endeavoring to achieve." These synonyms can be used in various contexts, from discussing business strategies to describing personal goals and motivations. As a writer or speaker, it's important to choose the most appropriate synonym based on the audience and context of the message.