"Am at loggerheads" is a phrase that indicates a state of conflict or disagreement between two or more parties. The antonyms of this phrase would therefore be words that express harmony, agreement or accord. These could include terms such as "in agreement", "on the same wavelength", "in sync" or "aligned". Other antonyms for "am at loggerheads" could be "peaceful", "calm" or "reconciled". These words suggest a state of calm and understanding rather than one of conflict and tension. When there is an absence of disagreements and conflicts, it paves the way for peaceful co-existence and progress towards common goals.