  We extend our previous work on the enhancement of the curvature spectrum
during inflation to the two-field case. We identify the slow-roll parameter
$\eta$ as the quantity that can trigger the rapid growth of perturbations. Its
two components, $\eta_\parallel$ along the background trajectory and
$\eta_\perp$ perpendicular to it, remain small during most of the evolution,
apart from short intervals during which they take large, positive or negative,
values. The typical reason for the appearance of strong features in
$\eta_\parallel$ is sharp steps or inflection points in the inflaton potential,
while $\eta_\perp$ grows large during sharp turns in field space. We focus on
the additive effect of several features leading to the resonant growth of the
curvature spectrum. Three or four features in the evolution of $\eta$ are
sufficient in order to induce an enhancement of the power spectrum by six or
seven orders of magnitude, which can lead to the significant production of
primordial black holes and stochastic gravitational waves. A big part of our
study focuses on understanding the evolution of the perturbations and the
resulting spectra through analytic means. The presence of multiple features in
the background evolution points to a more complex inflationary paradigm, which
is also more natural in the multi-field case. The critical examination of this
possibility is within the reach of experiment.
