  In recent work we showed that the relic dark matter abundance of QCD axions
can be altered when the Peccei-Quinn (PQ) field is coupled to very light
scalar/s, rendering the effective axion mass dynamical in the early universe.
In this work we develop this framework further, by introducing a new extended
symmetry group to protect the new particles' mass. We find that with a new
global $SO(N)$ symmetry, with large $N$, we can not only account for the
lightness of the new scalars, but we can reduce the axion relic abundance in a
technically natural way. This opens up the possibility of large PQ scales,
including approaching the GUT scale, and still naturally producing the correct
relic abundance of axions. Also, in these models the effective PQ scale is
relatively small in the very early universe, and so this can help towards
alleviating the isocurvature problem from inflation. Furthermore, instead of
possible over-closure from cosmic strings, the extended symmetry implies the
formation of non-topological textures which provide a relatively small
abundance.
