Not yet reviewed by Pith; the record is open.

With the growth of comparative exoplanetology, it is increasingly clear that investigating the relationships between inner and outer planets plays a key role in discriminating between competing formation and evolution models. To do so, it is important to probe the inner region of systems hosting long-period giants in search for undetected lower-mass planetary companions. In this work we present our results on the K-dwarf star BD-11~4672, already known to host a long-period giant planet, as the first output of a subsample of the GAPS programme specifically aimed at assessing the impact of inefficient migration of planets formed beyond the snowline by searching for Neptune-mass and super-Earths planetary companions of known longer-period giants. The high-precision HARPS-N observations of BD-11~4672 are used in conjunction with literature time series in order to search for additional inner planetary signals to be fitted using differential evolution Markov chain Monte Carlo. The long-term stability of the new orbital solutions is tested by N-body dynamical simulations. We report the detection of BD-11~4672~c, a new Neptune-mass planet with an orbital period of $74.20_{-0.08}^{+0.06}\,\rm{d}$, eccentricity $0.40_{-0.15}^{+0.13}$, semimajor axis $0.30\pm0.01\,\rm{au}$ and minimum mass $15.37_{-2.81}^{+2.97}\,M_\oplus$ orbiting slightly outside the inner edge of the optimistic circumstellar habitable zone. In order to assess its impact on the dynamical stability of the habitable zone we compute the angular momentum deficit of the system, showing that planet c has a severe negative impact on the stability of possible additional lower-mass temperate planets. The BD-11~4672 system is notable for its architecture, hosting both a long-period giant planet and an inner lower-mass planet, the latter being also among the most eccentric Neptune-mass planets known at similar periods.