  Strong-field quantum electrodynamics predicts electron-seeded
electron-positron pair cascades when the electric field in the rest-frame of
the seed electron approaches the Sauter-Schwinger field, i.e. $\eta =
E_{RF}/E_S \sim 1$. Electrons in the focus of next generation multi-PW lasers
are expected to reach this threshold. We identify three distinct cascading
regimes in the interaction of counter-propagating, circularly-polarised laser
pulses with a thin foil by performing a comprehensive scan over the laser
intensity (from $10^{23}$ -- $5\times10^{24}$\ Wcm$^{-2}$) and initial foil
target density (from $10^{26}$ -- $10^{31}$\ m$^{-3}$). For low densities and
intensities the number of pairs grows exponentially. If the intensity and
target density are high enough the number density of created pairs reaches the
relativistically-corrected critical density, the pair plasma efficiently
absorbs the laser energy (through radiation reaction) and the cascade
saturates. If the initial density is too high, such that the initial target is
overdense, the cascade is suppressed by the skin effect. We derive a
semi-analytical model which predicts that dense pair plasmas are endemic
features of these interactions for intensities above $10^{24}$ Wcm$^{-2}$
provided the target's relativistic skin-depth is longer than the laser
wavelength. Further, it shows that pair production is maximised in
near-critical-density targets, providing a guide for near-term experiments.
