  We explore the potential for the discovery of the triple-Higgs signal in the
$2b2l^{\pm}4j+E\!\!\!/$ decay channel at a $100$ TeV hadron collider. We
consider both the Standard Model and generic new-physics contributions,
described by an effective Lagrangian that includes higher-dimensional
operators. The selected subset of operators is motivated by composite-Higgs and
Higgs-inflation models. In the Standard Model, we perform both a parton-level
and a detector-level analysis. Although the parton-level results are
encouraging, the detector-level results demonstrate that this mode will be
really challenging. However, sizable contributions from new effective operators
can largely increase the cross section and/or modify the kinematics of the
Higgs bosons in the final state. Taking into account the projected constraints
from single and double Higgs-boson production, we propose benchmark points in
the new physics models for the measurement of the triple-Higgs boson final
state for future collider projects.
