The question of the dark matter nature is one of the important issues at the frontier of particle physics, astrophysics and cosmology. There are numerous models trying to explain the dark matter origin, assuming different underlying physical processes and proposing different candidates. One of the most simplistic dark matter candidates can arise due to the extension of the scalar electroweak sector. Such extensions are well motivated and could explain not only the dark matter origin but also other shortcomings of the Standard Model. The most natural way to accommodate a dark matter candidate in the extended scalar models, and to assure stability of dark matter, while controlling the number of free parameters is to assume an underlying symmetry. Governed by this, we review all possible cases of the $S_3$-symmetric three-Higgs-doublet models which can accommodate a scalar dark matter candidate. Within the model different cases arise due to different directions of vacua, which enforce different minimisation conditions. After classifying all possible dark matter candidates within the framework we explore two cases numerically.