  The discovery of planetary systems beyond the solar system has revealed a
diversity of architectures, most of which differ significantly from our system.
The initial detection of an exoplanet is often followed by subsequent
discoveries within the same system as observations continue, measurement
precision is improved, or additional techniques are employed. The HD 104067
system is known to consist of a bright K dwarf host star and a giant planet in
a $\sim$55 day period eccentric orbit. Here we report the discovery of an
additional planet within the HD 104067 system, detected through the combined
analysis of radial velocity data from the HIRES and HARPS instruments. The new
planet has a mass similar to Uranus and is in an eccentric $\sim$14 day orbit.
Our injection-recovery analysis of the radial velocity data exclude Saturn-mass
and Jupiter-mass planets out to 3 AU and 8 AU, respectively. We further present
TESS observations that reveal a terrestrial planet candidate ($R_p =
1.30\pm0.12$ $R_\oplus$) in a $\sim$2.2~day period orbit. Our dynamical
analysis of the three planet model shows that the two outer planets produce
significant eccentricity excitation of the inner planet, resulting in tidally
induced surface temperatures as high as $\sim$2600 K for an emissivity of
unity. The terrestrial planet candidate may therefore be caught in a tidal
storm, potentially resulting in its surface radiating at optical wavelengths.
