The phrase "be dominated by" can be replaced by a variety of synonyms depending on the context and the tone of the message. Some possible alternatives include "be controlled by," "be overpowered by," "be subject to," "be subjugated by," "be governed by," "be overwhelmed by," or "be influenced by." These variations all convey the idea of being under the authority or influence of something or someone else. Choosing the right synonym can help to clarify the nuances of a particular situation, whether it is a formal communication or a casual conversation.