  We obtain new BPS solutions of six-dimensional, N = 1 supergravity coupled to
a tensor multiplet. These solutions are sourced by multiple "superthreads"
carrying D1-D5-P charges and two magnetic dipole charges. These new solutions
are sourced by multiple threads with independent and arbitrary shapes and
include new shape-shape interaction terms. Because the individual superthreads
can be given independent profiles, the new solutions can be smeared together
into continuous "supersheets," described by arbitrary functions of two
variables. The supersheet solutions have singularities like those of the
three-charge, two dipole-charge generalized supertube in five dimensions and we
show how such five-dimensional solutions emerge from a very simple choice of
profiles. The new solutions obtained here also represent an important step in
finding superstrata, which are expected to play a role in the description of
black-hole microstates, due to their ability to store a large amount of entropy
in their two-dimensional profile.
