  Calculating multiple zeta values at arguments of any sign in a way that is
compatible with both the quasi-shuffle product as well as meromorphic
continuation, is commonly referred to as the renormalisation problem for
multiple zeta values. We consider the set of all solutions to this problem and
provide a framework for comparing its elements in terms of a free and
transitive action of a particular subgroup of the group of characters of the
quasi-shuffle Hopf algebra. In particular, this provides a transparent way of
relating different solutions at non-positive values, which answers an open
question in the recent literature.
