The phrase "taken up with" typically means to become preoccupied or absorbed with something. Synonyms for this phrase include "engrossed," "immersed," "absorbed," "consumed," "captivated," "enamored," "fascinated," and "fixated." When someone is taken up with a particular activity or idea, they are fully engaged and focused on it, to the point where it may be difficult to tear themselves away. Whether it's a new hobby, a work project, or a personal goal, being taken up with something can be both exhilarating and challenging. Whatever the case may be, these synonyms provide a variety of ways to express the state of being completely engrossed in something.