The level three multiverse is particular to a certain interpretation of quantum mechanics being Hugh Everett’s Many Worlds Interpretation. It is a mathematically simple model in support of unitary physics. Everything that can happen in the particle realm actually does happen. Each of the many worlds following a split represents one of the possible worlds remaining after the event which led to the split. There are no interactions between these worlds. No observer or inhabitant of them will notice anything about the other worlds.
Everett’s interpretation is not impossible due to the fact that we do not experience the continual splitting of our world. Observers would only view their level one multiverse, but the process of decoherence—which mimics wave function collapse while preserving unitary physics—prevents them from seeing the level three parallel copies of themselves. It is no more contradicted by our failure to experience the splitting than the theory that the earth rotates is contradicted by our failure to experience its movement. 
 Max Tegmark, “The Multiverse Hierarchy,” arXiv:0905.1283v1 (accessed March 15, 2011), 10.
 Some of the commentary is summarized by Karl Popper in Quantum Theory and the Schism in Physics, ed. W.W. Bartley, III (Totowa, NJ: Rowman and Littlefield, 1982): 91-2.