  Since Ginzburg and Landau's seminal work in 1950 superconducting states have
been classified by the hierarchy of the fundamental length scales of the
theory; the magnetic field penetration lengths and coherence lengths. In the
simplest single-component case they form a dimensionless ratio \kappa. As
pointed out by Ginzburg in 1952, in general the ratio depends on the direction
of the applied magnetic field due to material anisotropies. Single component
materials can therefore display type-1 superconductivity when the field is
applied in one direction and type-2 when the field is applied in a different
direction. In this paper we expand the above length scale analysis to
anisotropic multi-component superconductors, that can have multiple coherence
lengths as well as multiple magnetic field penetration lengths, leading to
unconvential length scale hierarchies. We demonstrate that the anisotropies in
multi-band superconductors cannot in general be rescaled, leading to new
regimes with various mixed hierarchies in different directions. For example, a
regime is possible, where for a field applied in a certain direction coherence
lengths are smaller than the magnetic field penetration lengths in one of the
perpendicular directions, where as the penetration lengths are lager in the
another direction. We demonstrate a new regime, where vortices form stripes in
the direction where coherence lengths exceed the magnetic field penetration
length and vortex cores overlap, while the vortex stripes repel each other in
the orthogonal direction where the magnetic field penetration length exceeds
the coherence lengths.
