  We study the orthogonal quantum groups satisfying the ``easiness'' assumption
axiomatized in our previous paper, with the construction of some new examples,
and with some partial classification results. The conjectural conclusion is
that the easy quantum groups consist of the previously known 14 examples, plus
of an hypothetical multi-parameter ``hyperoctahedral series'', related to the
complex reflection groups $H_n^s=\mathbb Z_s\wr S_n$. We discuss as well the
general structure, and the computation of asymptotic laws of characters, for
the new quantum groups that we construct.
