  The exploration of the scalar sector of the Standard Model is at the core of
current and future science programs at collider experiments, with increasing
focus on the self-interaction of the Higgs boson. This important parameter of
the Higgs sector can be measured in various channels, among the production of a
Higgs boson associated with a top-quark pair, $\bar{t}thh$. In this paper we
study this channel and its potential to measure or constrain the self-coupling
and possible new physics contributions at a future 100 TeV proton-proton
collider. Analysing this highly complex final state adds to the sensitivity for
enhanced self-coupling interactions, and we argue that a measurement of this
process is a necessity to constrain blind directions in the multi-dimensional
parameter space of well-motivated new physics scenarios.
