In explicit state model checking of concurrent systems, multi-core emptiness checks and partial order reductions (POR) are two major techniques to handle large state spaces. The first one tries to take advantage of multi-core architectures while the second one may decrease exponentially the size of the state space to explore. For checking LTL properties, Bloemen and van de Pol [2] shown that the best performance is currently obtained using their multi-core SCC-based emptiness check. However, combining the latest SCC-based algorithm with POR is not trivial since a condition on cycles, the proviso, must be enforced on an algorithm which processes collaboratively cycles. In this paper, we suggest a pessimistic approach to tackle this problem for liveness properties. For safety ones, we propose an algorithm which takes benefit from the information computed by the SCC-based algorithm. We also present new parallel provisos for both safety and liveness properties that relies on other multi-core emptiness checks. We observe that all presented algorithms maintain good reductions and scalability.