  We present radial velocity measurements of the very bright ($V\sim5.7$)
nearby F star, DMPP-4 (HD 184960). The anomalously low Ca II H&K emission
suggests mass loss from planets orbiting a low activity host star. Periodic
radial velocity variability with $\sim 10$ ms$^{-1}$ amplitude is found to
persist over a $>4$ year timescale. Although the non-simultaneous photometric
variability in four TESS sectors supports the view of an inactive star, we
identify periodic photometric signals and also find spectroscopic evidence for
stellar activity. We used a posterior sampling algorithm that includes the
number of Keplerian signals, $N_\textrm{p}$, as a free parameter to test and
compare (1) purely Keplerian models (2) a Keplerian model with linear activity
correlation and (3) Keplerian models with Gaussian processes. A preferred
model, with one Keplerian and quasi-periodic Gaussian process indicates a
planet with a period of $P_\textrm{b} = 3.4982^{+0.0015}_{-0.0027}$ d and
corresponding minimum mass of $m_\textrm{b}\,\textrm{sin}\,i =
12.2^{+1.8}_{-1.9}$ M$_\oplus$. Without further high time resolution
observations over a longer timescale, we cannot definitively rule out the
purely Keplerian model with 2 candidates planets with $P_\textrm{b} =
2.4570^{+0.0026}_{-0.0462}$ d, minimum mass $m_\textrm{b}\,\textrm{sin}\,i =
8.0^{+1.1}_{-1.5}$ M$_\oplus$ and $P_\textrm{c} = 5.4196^{+0.6766}_{-0.0030}$ d
and corresponding minimum mass of $m_\textrm{b}\,\textrm{sin}\,i =
12.2^{+1.4}_{-1.6}$ M$_\oplus$. The candidate planets lie in the region below
the lower-envelope of the Neptune Desert. Continued mass loss may originate
from the highly irradiated planets or from an as yet undetected body in the
system.
