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 ∼55 days 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 (RV) data from the High Resolution Echelle Spectrometer and High Accuracy Radial velocity Planet Searcher instruments. The new planet has a mass similar to Uranus and is in an eccentric ∼14 days orbit. Our injection-recovery analysis of the RV data exclude Saturn-mass and Jupiter-mass planets out to 3 au and 8 au, respectively. We further present Transiting Exoplanet Survey Satellite observations that reveal a terrestrial planet candidate (Rp = 1.30 ± 0.12 R⊕) in a ∼2.2 days 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 ∼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.