  Force-free equilibria containing two vertically arranged magnetic flux ropes
of like chirality and current direction are considered as a model for split
filaments/prominences and filament-sigmoid systems. Such equilibria are
constructed analytically through an extension of the methods developed in Titov
& D\'emoulin (1999) and numerically through an evolutionary sequence including
shear flows, flux emergence, and flux cancellation in the photospheric
boundary. It is demonstrated that the analytical equilibria are stable if an
external toroidal (shear) field component exceeding a threshold value is
included. If this component decreases sufficiently, then both flux ropes turn
unstable for conditions typical of solar active regions, with the lower rope
typically being unstable first. Either both flux ropes erupt upward, or only
the upper rope erupts while the lower rope reconnects with the ambient flux low
in the corona and is destroyed. However, for shear field strengths staying
somewhat above the threshold value, the configuration also admits evolutions
which lead to partial eruptions with only the upper flux rope becoming unstable
and the lower one remaining in place. This can be triggered by a transfer of
flux and current from the lower to the upper rope, as suggested by the
observations of a split filament in Paper~I (Liu et al. 2012). It can also
result from tether-cutting reconnection with the ambient flux at the X-type
structure between the flux ropes, which similarly influences their stability
properties in opposite ways. This is demonstrated for the numerically
constructed equilibrium.
