  Traditionally, superconductors are categorized as type-I or type-II. Type-I
superconductors support only Meissner and normal states, while type-II
superconductors form magnetic vortices in sufficiently strong applied magnetic
fields. Recently there has been much interest in superconducting systems with
several species of condensates, in fields ranging from Condensed Matter to High
Energy Physics. Here we show that the type-I/type-II classification is
insufficient for such multicomponent superconductors. We obtain solutions
representing thermodynamically stable vortices with properties falling outside
the usual type-I/type-II dichotomy, in that they have the following features:
(i) Pippard electrodynamics, (ii) interaction potential with long-range
attractive and short-range repulsive parts, (iii) for an n-quantum vortex, a
non-monotonic ratio E(n)/n where E(n) is the energy per unit length, (iv)
energetic preference for non-axisymmetric vortex states, "vortex molecules".
Consequently, these superconductors exhibit an emerging first order transition
into a "semi-Meissner" state, an inhomogeneous state comprising a mixture of
domains of two-component Meissner state and vortex clusters.
