  This paper considers secular interactions within multi-planet systems. In
particular we consider dynamical evolution of known planetary systems resulting
from an additional hypothetical planet on an eccentric orbit. We start with an
analytical study of a general two-planet system, showing that a planet on an
elliptical orbit transfers all of its eccentricity to an initially circular
planet if the two planets have comparable orbital angular momenta. Application
to the single Super-Earth system HD38858 shows that an additional hypothetical
planet below current radial velocity (RV) constraints with
{\textit{Msini}}=3-10M$_\oplus$, semi-major axis 1-10au and eccentricity
0.2-0.8 is unlikely to be present from the eccentricity that would be excited
in the known planet (albeit cyclically). However, additional planets in
proximity to the known planet could stabilise the system against secular
perturbations from outer planets. Moreover these additional planets can have an
{\textit{Msini}} below RV sensitivity and still affect their neighbours. For
example, application to the two Super-Earth system 61Vir shows that an
additional hypothetical planet cannot excite high eccentricities in the known
planets, unless its mass and orbit lie in a restricted area of parameter space.
Inner planets in HD38858 below RV sensitivity would also modify conclusions
above about excluded parameter space. This suggests that it may be possible to
infer the presence of additional stabilising planets in systems with an
eccentric outer planet and an inner planet on an otherwise suspiciously
circular orbit. This reinforces the point that the full complement of planets
in a system is needed to assess its dynamical state.
