Existence of Maximin Share (MMS) Allocations in Mixed Manna Settings

An MMS allocation exists as long as the number of items m is at most n + 5, and either (i) every agent is a chores agent, or (ii) there exists a non-negative agent. Additionally, for n ≤ 3 agents, an MMS allocation exists as long as m ≤ n + 5, regardless of the types of agents.