  Giant gaseous planets often reside on orbits in sufficient proximity to their
host stars for the planetary quadrupole gravitational field to become
non-negligible. In presence of an additional planetary companion, a precise
characterization of the system's orbital state can yield meaningful constraints
on the transiting planet's interior structure. However, such methods can
require a very specific type of system. This paper explores the dynamic range
of applicability of these methods and shows that interior structure
calculations are possible for a wide array of orbital architectures. The
HAT-P-13 system is used as a case study, and the implications of perturbations
arising from a third distant companion on the feasibility of an interior
calculation are discussed. We find that the method discussed here is likely to
be useful in studying other planetary systems, allowing the possibility of an
expanded survey of the interiors of exoplanets.
