  We study incoherent diffractive production of two and three jets in
electron-nucleus deep inelastic scattering (DIS) at small
$x_{\scriptscriptstyle \rm Bj}$ using the color dipole picture and the
effective theory of the Color Glass Condensate (CGC). We consider color
fluctuations in the CGC weight-function as the source of the nuclear break-up
and the associated momentum transfer $\sqrt{|t|}$. We focus on the regime in
which the two jets are almost back-to-back in transverse space and have
transverse momenta $P_{\perp}$ much larger than both the momentum transfer and
the saturation scale $Q_s$. The cross section for producing such a hard dijet
is parametrically dominated by large size fluctuations in the projectile
wave-function that scatter strongly and for which a third, semi-hard, jet
appears in the final state. The 2 + 1 jets cross section can be written in a
factorized form in terms of incoherent quark and gluon diffractive transverse
momentum distributions (DTMDs) when the third jet is explicit, or incoherent
diffractive parton distribution functions (DPDFs) when the third jet is
integrated over. We find that the DPDFs and the corresponding cross section
saturate logarithmically when $|t| \ll Q_s^2$, while they fall like $1/|t|^2$
in the regime $Q_s^2 \ll |t| \ll P_{\perp}^2$. We further show that there is no
angular correlation between the hard jet momentum and the momentum transfer.
For typical EIC kinematics the 2 jets and 2 + 1 jets cross sections are of the
same order.
