  In this paper, we develop a structure theory for generalized spectral
sequences, which are derived from chain complexes that are filtered over
arbitrary partially ordered sets. Also, a more general construction method
reminiscent of exact couples is studied, together with examples where they
arise naturally. As for ordinary spectral sequences we will see differentials
and group extensions, however the real power comes from the appearance of
natural isomorphims between pages of differing indices.
  The constructions reveal finer invariants than ordinary spectral sequences,
and they connect to other fields such as Fary functors and perverse sheaves.
They are based on a natural index scheme, which allows us to obtain new results
even in the standard case of Z-filtered chain complexes, e.g. a useful
criterion for a product structure for Grothendieck's spectral sequences, and
news paths to connect the first or second page to the limit.
  This turns out to yield the right framework for unifying several spectral
sequences that one would usually apply one after another. Examples that we work
out are successive Leray--Serre spectral sequences, the Adams--Novikov spectral
sequence following the chromatic spectral sequence, successive Grothendieck
spectral sequences, and successive Eilenberg--Moore spectral sequences.
