The phrase "was on one case" implies that someone was focused on a specific task or investigation. To find antonyms for this phrase, we can look for words that suggest a lack of focus or direction. Some possible antonyms include "unfocused," "uncommitted," "divided," or "scattered." Alternatively, we could look for words that suggest a lack of intensity or urgency, such as "relaxed," "casual," or "unconcerned." However, it's worth noting that antonyms for this phrase may depend on the specific context and connotations of the original phrase, so the best antonyms will vary depending on the situation.