  We investigate the correlated state of Ce$_2$Hf$_2$O$_7$ using neutron
scattering, finding signatures of correlations of both dipolar and octupolar
character. A dipolar inelastic signal is also observed, as expected for spinons
in a quantum spin ice (QSI). Fits of thermodynamic data using exact
diagonalization methods indicate that the largest interaction is an octupolar
exchange, with a strength roughly twice as large as other terms. A hierarchy of
exchange interactions with dominant octupolar and significant dipolar exchange,
still in the octupolar QSI phase, rationalises neutron scattering observations.
Our results reveal a `quantum multipolar liquid' where correlations involve
multiple terms in moment series expansion, opening questions about their
intertwining and possible hierarchy.
