The reason quadruple eclipses can never happen on Jupiter is because of the 1:2:4 orbital resonance between Io, Europa, and Ganymede. As far as I know this isn't a problem for Saturn's moons.
From Wikipedia's Solar eclipses on Saturn:
Seven of Saturn's satellites – Janus, Mimas, Enceladus, Tethys, Rhea, Dione and Titan – are large enough and near enough to eclipse or occult the Sun, or in other words to cast an umbra on Saturn.
Of the 7 listed above, Mimas and Tethys are in a 2:1 orbital resonance and so are Enceladus and Dione, however that doesn't stop either pair (or all 4 together) from eclipsing Saturn at the same time.
So, in theory, it is possible for all 7 moons to more or less line up together. Does this mean that during eclipse season on Saturn, there can be a septuple eclipse? If so, when is the next one going to happen?