Existence of symEF(n-1) allocations

Let an instance consist of $n$ agents and $m$ items. A symEF$(n-1)$ allocation is an allocation satisfying symmetric envy-freeness up to $n-1$ items. SymEF$(n-1)$ existence conjecture. For any instance with $n$ agents and $m$ items, a symEF$(n-1)$ allocation exists. The claim is proposed as a sufficient condition for the existence of weaker symmetric fairness solutions and is open.