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With the growth of comparative exoplanetology, it is increasingly clear thatinvestigating the relationships between inner and outer planets plays a keyrole in discriminating between competing formation and evolution models. To doso, it is important to probe the inner region of systems hosting long-periodgiants in search for undetected lower-mass planetary companions. In this workwe present our results on the K-dwarf star BD-11~4672, already known to host along-period giant planet, as the first output of a subsample of the GAPSprogramme specifically aimed at assessing the impact of inefficient migrationof planets formed beyond the snowline by searching for Neptune-mass andsuper-Earths planetary companions of known longer-period giants. Thehigh-precision HARPS-N observations of BD-11~4672 are used in conjunction withliterature time series in order to search for additional inner planetarysignals to be fitted using differential evolution Markov chain Monte Carlo. Thelong-term stability of the new orbital solutions is tested by N-body dynamicalsimulations. We report the detection of BD-11~4672~c, a new Neptune-mass planetwith 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 ofthe optimistic circumstellar habitable zone. In order to assess its impact onthe dynamical stability of the habitable zone we compute the angular momentumdeficit of the system, showing that planet c has a severe negative impact onthe stability of possible additional lower-mass temperate planets. TheBD-11~4672 system is notable for its architecture, hosting both a long-periodgiant planet and an inner lower-mass planet, the latter being also among themost eccentric Neptune-mass planets known at similar periods.

The GAPS Programme at TNG -- XXIV. An eccentric Neptune-mass planet near the inner edge of the BD-11 4672 habitable zone