  Multi-electron dynamics in atoms and molecules very often occur on sub- to
few-femtosecond timescales. The available intensities of extreme-ultraviolet
(XUV) attosecond pulses have previously only allowed the time-resolved
investigation of two-photon, two-electron interactions. Here we demonstrate
attosecond control over double and triple ionization of argon atoms involving
the absorption of up to five XUV photons. In an XUV-pump XUV-probe measurement
using a pair of attosecond pulse trains (APTs), the Ar$^{2+}$ ion yield
exhibits a weak delay dependence, showing that its generation predominantly
results from the sequential emission of two electrons by photoabsorption from
the two APTs. In contrast, the Ar$^{3+}$ ion yield exhibits strong modulations
as a function of the delay, which is a clear signature of the simultaneous
absorption of at least two XUV photons. The experimental results are well
reproduced by numerical calculations that provide detailed insights into the
ionization dynamics. Our results open up new opportunities for the
investigation and control of multi-electron dynamics and complex electron
correlation mechanisms on extremely short timescales.
