The antonyms of the phrase "climbing all over" are quite straightforward. The phrase simply means to move about in a restless or chaotic manner. The opposite would be to remain stationary, calm, or still. Other antonyms for this phrase could be to relax, sit still, or remain composed. These antonyms are often associated with a sense of tranquility or serenity, and can be beneficial in situations where chaotic movement would be disruptive. Whether in a classroom, a meeting, or a social setting, employing these antonyms can help bring a sense of peace and order to the situation.