  There are well-known criteria on the potential and field-space geometry for
determining if slow-roll, slow-turn, multi-field inflation is possible.
However, even though it has been a topic of much recent interest, slow-roll,
rapid-turn inflation only has such criteria in the restriction to two fields.
In this work, we generalize the two-field, rapid-turn inflationary attractor to
an arbitrary number of fields. We quantify a limit, which we dub extreme
turning, in which rapid-turn solutions may be found efficiently and develop
methods to do so. In particular, simple results arise when the covariant
Hessian of the potential has an eigenvector in close alignment with the
gradient -- a situation we find to be common and we prove generic in two-field
hyperbolic geometries. We verify our methods on several known rapid-turn models
and search two type-IIA constructions for rapid-turn trajectories. For the
first time, we are able to efficiently search for these solutions and even
exclude slow-roll, rapid-turn inflation from one potential.
