Although the present-day orbital distribution of minor bodies that go around the Sun between the orbit of Neptune and the Kuiper Cliff is well understood, past ∼50 au from the Sun, our vision gets blurred as objects become fainter and fainter and their orbital periods span several centuries. Deep imaging using the largest telescopes can overcome the first issue but the problems derived from the second one are better addressed using data analysis techniques. Here, we make use of the heliocentric range and range-rate of the known Kuiper belt objects and their uncertainties to identify structures in orbital parameter space beyond the Kuiper Cliff. The distribution in heliocentric range there closely resembles that of the outer main asteroid belt with a gap at ∼70 au that may signal the existence of a dynamical analogue of the Jupiter family comets. Outliers in the distribution of mutual nodal distances suggest that a massive perturber is present beyond the heliopause.