  Using a spectrally resolved electron interferometry technique, we measure
photoionization time delays between the $3s$ and $3p$ subshells of argon over a
large 34-eV energy range covering the Cooper minima in both subshells. The
observed strong variations of the $3s-3p$ delay difference, including a sign
change, are well reproduced by theoretical calculations using the Two-Photon
Two-Color Random Phase Approximation with Exchange. Strong shake-up channels
lead to photoelectrons spectrally overlapping with those emitted from the $3s$
subshell. These channels need to be included in our analysis to reproduce the
experimental data. Our measurements provide a stringent test for
multielectronic theoretical models aiming at an accurate description of
inter-channel correlation.
