  We consider Higgs boson pair production at a future proton collider with
centre-of-mass energy of 100 TeV, focusing on rare final states that include a
bottom-anti-bottom quark pair and multiple isolated leptons: $hh \rightarrow
(b\bar{b}) + n \ell + X$, $n = \{2,4\}$, $X = \{ E_T^\mathrm{miss}, \gamma,
-\}$. We construct experimental search strategies for observing the process
through these channels and make suggestions on the desired requirements for the
detector design of the future collider.
