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The combination of detection techniques enhances our ability to identify companions orbiting nearby stars. We employed high-contrast imaging to constrain mass and separation of possible companions responsible for the significant proper motion anomalies of the nearby stars HIP 11696, HIP 47110, and HIP 36277. These targets were observed using the LBT's high-contrast camera, SHARK-NIR, in H band using a Gaussian coronagraph, and with the LMIRCam instrument in the L ' band and using a vAPP coronagraph. Both observations were conducted simultaneously. Additionally, constraints at short separations from the host star are derived analysing the renormalized unit weight error values from the Gaia catalogue. We find that the companion responsible for the anomaly signal of HIP 11696 is likely positioned at a distance from 2.5 to 28 astronomical units from its host. Its mass is estimated to be between 4 and 16 Jupiter masses, with the greater mass possible only at the upper end of the separation range. Similar limits were obtained for HIP 47110 where the companion should reside between 3 and 30 au with a mass between 3 and 10 MJup. For HIP 36277, we identified a faint stellar companion at large separation, though it might be substellar depending on the assumed age for the star. Considering the older age, this object accounts for the absolute value of the PMa vector but not for its direction. Additionally, we found a substellar candidate companion at a closer separation that could explain the PMa signal, considering a younger age for the system. [ABSTRACT FROM AUTHOR]