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Sirius-like systems are wide binaries composed of a white dwarf (WD) and a companion of a spectral type earlier than M0. The WD progenitor evolves in isolation, but its wind during the AGB phase pollutes the companion surface and transfers some angular momentum. Within SHINE survey that uses SPHERE at the VLT, we acquired images of HD2133, HD114174, and CD-567708 and combined this data with high resolution spectra of the primaries, TESS, and literature data. We performed accurate abundance analyses for the MS. We found brighter J and K magnitudes for HD114174B than obtained previously and extended the photometry down to 0.95 micron. Our new data indicate a higher temperature and then shorter cooling age (5.57+/-0.02 Gyr) and larger mass (0.75+/-0.03 Mo) for this WD than previously assumed. This solved the discrepancy previously found with the age of the MS star. The two other WDs are less massive, indicating progenitors of ~1.3 Mo and 1.5-1.8 Mo for HD2133B and CD-56 7708B, respectively. We were able to derive constraints on the orbit for HD114174 and CD-56 7708. The composition of the MS stars agrees fairly well with expectations from pollution by the AGB progenitors of the WDs: HD2133A has a small enrichment of n-capture elements, which is as expected for pollution by an AGB star with a mass <1.5 Mo; CD-56 7708A is a previously unrecognized mild Ba-star, which is expected due to pollution by an AGB star with a mass in the range of 1.5-3.0 Mo; and HD114174 has a very moderate excess of n-capture elements, which is in agreement with the expectation for a massive AGB star to have a mass >3.0 Mo. On the other hand, none of these stars show the excesses of C that are expected to go along with those of n-capture elements. This might be related to the fact that these stars are at the edges of the mass range where we expect nucleosynthesis related to thermal pulses.