  To date, studies of $\textit{Laplace Surface}$ dynamics have concerned
themselves with test particle orbits of fixed shape and orientation in the
combined field of an oblate central body (to which the particle is bound) and a
distant, inclined, companion which is captured to quadrupolar order. While
amply sufficient for satellites around planets on near-circular orbits, the
quadrupolar approximation fails to capture essential dynamical features induced
by a wide binary companion (be it a star, a planet or a black hole) on a fairly
eccentric orbit. With similar such astronomical settings in mind, we extend the
classical Laplace framework to higher multipoles, and map out the backbone of
stationary orbits, now complexified by the broken axial symmetry. Eccentric and
inclined Laplace equilibria, which had been presaged in systems of large enough
mutual inclination, are here delineated over a broad range of mutually inclined
perturbations. We recover them for test particles in the field of a hot Jupiter
and a wide eccentric stellar binary, highlighting their relevance for the
architecture of multi-planet systems in binaries. We then extend and deploy our
machinery closer to home, as we consider the secular dynamics of
Trans-Neptunian Objects (TNOs) in the presence of a putative ninth planet. We
show how generalized Laplace equilibria seed islands for Trans-Neptunian
objects to be sheltered around, islands within chaotic seas which we capture
via Poincar$\'{e}$ sections, while highlighting a beautiful interplay between
Laplace and Kozai-Lidov secular dynamical structures. An eminently classical
tale revived for the exo-planetary 21st century!
