The monkey (원숭이, wonsungi) is read through cleverness and quick problem-solving, similar in spirit to the rabbit, but with an extra note of caution baked into Korean culture more broadly: the well-known saying "원숭이도 나무에서 떨어진다" ("even a monkey falls from a tree") is used constantly in everyday Korean to mean that even the most skilled person can make a mistake, and that same caution shapes the dream's reading.
A monkey solving a problem, using a tool, or outsmarting another animal in the dream is read as a clever solution arriving in waking life — wit succeeding where brute effort wouldn't have. This is read favorably, close to the rabbit's cleverness-based fortune, but specifically tied to skill and expertise rather than luck.
A monkey falling, stumbling, or failing at something it should easily manage is read almost literally through the saying above — a warning against overconfidence, especially in an area where you already consider yourself skilled or experienced. It's a rare case in this tradition where the folk dream reading and a common everyday idiom line up so directly.
Multiple monkeys playing together is read more lightly, generally as a busy, social period ahead rather than carrying much weight either way — one of the more neutral entries in the whole animal category.