  We present a parallel version of Sch\"onhage's Storage Modification Machine,
the Multiway Storage Modification Machine (MWSMM). Like the alternative
Association Storage Modification Machine of Tromp and van Emde Boas, MWSMMs
recognize in polynomial time what Turing Machines recognize in polynomial
space. Falling thus into the Second Machine Class, the MWSMM is a parallel
machine model conforming to the Parallel Computation Thesis. We illustrate
MWSMMs by a simple implementation of Wolfram's String Substitution System.
