Studies of the Higgs boson pair production and decays into $bb\gamma\gamma$, $bb\tau\tau$, and $bb\mathrm{W}\mathrm{W}$ final states are presented. The studies are performed assuming the operational conditions of the High-Luminosity LHC, with an integrated luminosity of 3000~$\mathrm{fb}^{-1}$, and the upgraded CMS experiment. Combining the studies of $bb\gamma\gamma$ and $bb\tau\tau$ final states, the expected significance for Higgs boson pair production is 1.9 standard deviation. The resulting expected uncertainty in the signal yield is $54\%$. The benefits of the CMS Phase-II upgrade, to meet the challenges presented by the high luminosity environment, are emphasized. $\textit{Version of November 15, 2015: additional references included.}$

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