  When doped with a high density of mobile charge carriers, monolayer
transition-metal dichalcogenide (TMD) semiconductors can host new types of
composite many-particle exciton states that do not exist in conventional
semiconductors. Such multi-particle bound states arise when a photoexcited
electron-hole pair couples to not just a single Fermi sea that is
quantum-mechanically distinguishable (as for the case of conventional charged
excitons or trions), but rather couples simultaneously to \textit{multiple}
Fermi seas, each having distinct spin and valley quantum numbers. Composite
six-particle ``hexciton'' states were recently identified in electron-doped
WSe$_2$ monolayers, but under suitable conditions they should also form in all
other members of the monolayer TMD family. Here we present spectroscopic
evidence demonstrating the emergence of many-body hexcitons in charge-tunable
WS$_2$ monolayers (at the A-exciton) and MoSe$_2$ monolayers (at the
B-exciton). The roles of distinguishability and carrier screening on the
stability of hexcitons are discussed.
