  We develop a notion of ellipsitomic associators by means of operad theory. We
take this opportunity to review the operadic point-of-view on Drinfeld
associators and to provide such an operadic approach for elliptic associators
too. We then show that ellipsitomic associators do exist, using the monodromy
of the universal ellipsitomic KZB connection, that we introduced in a previous
work. We finally relate the KZB ellipsitomic associator to certain Eisenstein
series associated with congruence subgroups of $SL_2(\mathbb{Z})$, and to
twisted elliptic multiple zeta values.
