Casting one's net is a commonly used phrase that refers to trying to achieve something by taking a chance on various opportunities or potential outcomes. There are several synonyms that can be used to convey similar meaning, such as taking a shot, making an attempt, testing the waters, or throwing the dice. Each phrase suggests a level of risk-taking or chance involved in the process of achieving a goal. Other alternatives include exploring options, seeking opportunities, or pursuing possibilities. The use of these terms might depend on the context in which they are used, but they all suggest an open-minded and optimistic approach to achieving a desired outcome.