One of the most frequently used inference services of description logic reasoners classifies all named classes of OWL ontologies into a subsumption hierarchy. Due to emerging OWL ontologies from the web community consisting of up to hundreds of thousand of named classes and the increasing availability of multi-processor and multi- or many-core computers, we extend our work on parallel TBox classification and propose a new algorithm that is sound and complete and demonstrates in a first experimental evaluation a low overhead w.r.t. subsumption tests (less than 3%) if compared with sequential classification.