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In recent decades, thousands of substellar companions have been discovered with both indirect and direct methods of detection. In this paper, we focus our attention on substellar companions detected with the direct imaging technique, with the primary goal of investigating their close surroundings and looking for additional companions and satellites, as well as disks and rings. Any such discovery would shed light on many unresolved questions, particularly with regard to their possible formation mechanisms. To reveal bound features of directly imaged companions we need to suppress the contribution from the source itself. Therefore, we developed a method based on the negative fake companion (NEGFC) technique that first estimates the position in the field of view (FoV) and the flux of the imaged companion, then subtracts a rescaled model point spread function (PSF) from the imaged companion. Next it performs techniques, such as angular differential imaging (ADI), to further remove quasi-static patterns of the star. We applied the method to the sample of substellar objects observed with SPHERE during the SHINE GTO survey. Among the 27 planets and brown dwarfs we analyzed, we detected a possible point source close to DH Tau B. This candidate companion was detected in four different SPHERE observations, with an estimated mass of $\sim 1$ M\textsubscript{Jup}, and a mass ratio with respect to the brown dwarf of $1/10$. This binary system, if confirmed, would be the first of its kind, opening up interesting questions for the formation mechanism, evolution, and frequency of such pairs. In order to address the latter, the residuals and contrasts reached for 25 companions in the sample of substellar objects observed with SPHERE were derived. If the DH Tau Bb companion is real, the binary fraction obtained is $\sim 7\%$, which is in good agreement with the results obtained for field brown dwarfs.