  In this two-part essay, we distinguish several senses in which general
relativity has been regarded as "locally special relativistic". In Part 1, we
focused on senses in which a relativistic spacetime may be said to be "locally
(approximately) Minkowskian". Here, in Part 2, we consider what it might mean
to say that a matter theory is "locally special relativisitc". We isolate and
evaluate three criteria in the literature and show that they are incompatible:
matter theories satisfying one will generally violate others. We then consider
what would happen if any of those criteria failed for a given theory.
