  We extend the classification of nearest neighbour walks in the quarter plane
to models in which multiplicities are attached to each direction in the step
set. Our study leads to a small number of infinite families that completely
characterize all the models whose associated group is D4, D6, or D8. These
families cover all the models with multiplicites 0, 1, 2, or 3, which were
experimentally found to be D-finite --- with three noteworthy exceptions.
