Using large data samples of di-muon events, CMS has performed detailed measurements in the field of Hadron Spectroscopy. Recent results include the search for an unexpected narrow $B_s \, \pi^{\pm}$ structure claimed by the $D\emptyset$ Collaboration and named $X(5568)$ (its interest resides in its possible interpretation as a compact hadronic state composed of four different quark flavours: udsb), the confirmation of the $X(4140) \rightarrow J/\psi \, \phi$ reported by CDF, a study of $X(3872)$ production properties and a search for the its bottomonium partner. In this realm, potential resonances have been predicted with a double quarkonium in the final states, such as heavy quark tetra-quarks governed by strong interaction. The first observation of $\Upsilon(1S)$ pair production has been recently performed and the study of $J/\psi$ pair final state produced in proton-proton collisions at $\sqrt{s} = 7$ TeV is foreseen to be extended to a center-of-mass of 8 TeV providing the total and differential cross sections measured in a phase space defined by the individual $J/\psi$ transverse momentum and rapidity. These observations allow us to access, for the first time, to the high-transverse-momentum region of $J/\psi$ pair production where model predictions are not yet established.