This paper describes Path-Moose, a scalable tree-based shortest path bridging protocol. Both ARP-Path and Path-Moose protocols belong to a new category of bridges that we name All-path, because all paths of the network are explored simultaneously with a broadcast frame distributed over all network links to find a path or set a multicast tree. Path-Moose employs the ARP-based low latency routing mechanism of the ARP-Path protocol on a bridge basis instead of a per-single-host basis. This increases scalability by reducing forwarding table entries at core bridges by a factor of fifteen times for big data center networks and achieves a faster reconfiguration by an approximate factor of ten. Reconfiguration time is significantly shorter than ARP-Path (zero in many cases) because, due to the sharing of network paths by the hosts connected to same edge bridges, when a host needs the path it has already been recovered by another user of the path. Evaluation through simulations shows protocol correctness and confirms the theoretical evaluation results.