Future solar missions and ground-based telescopes aim to understand the magnetism of the solar chromosphere. We performed a supporting study in Quintero Noda et al. focused on the infrared Ca (II) 8542 angstrom line and we concluded that it is one of the best candidates because it is sensitive to a large range of atmospheric heights, from the photosphere to the middle chromosphere. However, we believe that it is worth trying to improve the results produced by this line observing additional spectral lines. In that regard, we examined the neighbourhood solar spectrum looking for spectral lines which could increase the sensitivity to the atmospheric parameters. Interestingly, we discovered several photospheric lines which greatly improve the photospheric sensitivity to the magnetic field vector. Moreover, they are located close to a second chromospheric line which also belongs to the Ca (II) infrared triplet, i.e. the Ca (II) 8498 angstrom line, and enhances the sensitivity to the atmospheric parameters at chromospheric layers. We conclude that the lines in the vicinity of the Ca (II) 8542 A line not only increase its sensitivity to the atmospheric parameters at all layers, but also they constitute an excellent spectral window for chromospheric polarimetry.