Antonyms for the phrase "climbs all over" include words like "descends," "settles," "remains grounded," and "stays put." Each of these phrases suggests the opposite of the intense, frenzied activity of climbing all over something. Descending implies a controlled or gradual lowering, while settling suggests a comfortable or steady resting state. Remaining grounded and staying put both convey a sense of stability and quietness, with no movement beyond what is necessary. Depending on the context, any of these antonyms could be used to convey a sense of stillness or calmness.