  We investigate the interactions of large composite dark matter (DM) states
with the Standard Model (SM) sector. Elastic scattering with SM nuclei can be
coherently enhanced by factors as large as A^2, where A is the number of
constituents in the composite state (there exist models in which DM states of
very large A > 10^8 may be realised). This enhancement, for a given direct
detection event rate, weakens the expected signals at colliders by up to 1/A.
Moreover, the spatially extended nature of the DM states leads to an
additional, characteristic, form factor modifying the momentum dependence of
scattering processes, altering the recoil energy spectra in direct detection
experiments. In particular, energy recoil spectra with peaks and troughs are
possible, and such features could be confirmed with only O(50) events,
independently of the assumed halo velocity distribution. Large composite states
also generically give rise to low-energy collective excitations potentially
relevant to direct detection and indirect detection phenomenology. We compute
the form factor for a generic class of such excitations - quantised surface
modes - finding that they can lead to coherently-enhanced, but generally
sub-dominant, inelastic scattering in direct detection experiments. Finally, we
study the modifications to capture rates in astrophysical objects that follow
from the elastic form factor, as well as the effects of inelastic interactions
between DM states once captured. We argue that inelastic interactions may lead
to the DM collapsing to a dense configuration at the centre of the object.
