  Context. Planets with radii of between 2-4 RE closely orbiting solar-type
stars are of significant importance for studying the transition from rocky to
giant planets.
  Aims. Our goal is to determine the mass of a transiting planet around the
very bright F6 star HD 73344 . This star exhibits high activity and has a
rotation period that is close to the orbital period of the planet.
  Methods. The transiting planet, initially a K2 candidate, is confirmed
through TESS observations . We refined its parameters and rule out a false
positive with Spitzer observations. We analyzed high-precision RV data from the
SOPHIE and HIRES spectrographs. We conducted separate and joint analyses using
the PASTIS software. We used a novel observing strategy, targeting the star at
high cadence for two consecutive nights with SOPHIE to understand the
short-term stellar variability. We modeled stellar noise with two Gaussian
processes.
  Results. High-cadence RV observations provide better constraints on stellar
variability and precise orbital parameters for the transiting planet. The
derived mean density suggests a sub-Neptune-type composition, but uncertainties
in the planet's mass prevent a detailed characterization. In addition, we find
a periodic signal in the RV data that we attribute to the signature of a
nontransiting exoplanet, without totally excluding the possibility of a
nonplanetary origin. Dynamical analyses confirm the stability of the two-planet
system and provide constraints on the inclination of the candidate planet;
these findings favor a near-coplanar system.
  Conclusions. While the transiting planet orbits the bright star at a short
period, stellar activity prevented us from precise mass measurements. Long-term
RV tracking of this planet could improve this measurement, as well as our
understanding of the activity of the host star.
