The antonyms for the phrase "keep distance" can be "get closer" or "approach". These antonyms imply a movement towards someone or something, rather than maintaining a safe distance. Another set of antonyms could be "mingling" or "crowding", which suggest being in close proximity without any space between individuals. To "mix in" or "merge" would also be antonyms to "keep distance", as they signify a coming together rather than a separation. Antonyms to "keep distance" vary depending on the context, but they generally imply the act of reducing physical, emotional or social distance between people or objects.