  Disproportionation in 3d compounds can give rise to an unconventional
electron-hole Bose liquid with a very rich phase diagram from a Bose metal,
charge ordering insulator to an inhomogeneous Bose superfluid. Optimal
conditions for the disproportionation driven high-T_c superconductivity are
shown to realize only for several Jahn-Teller d^n configurations that permit
the formation of well defined local composite bosons. These are the high-spin
d^4, low-spin d^7, and d^9 configurations given the octahedral crystal field,
and the d^1, high-spin d^6 configurations given the tetrahedral crystal field.
The disproportionation reaction has a peculiar anti-Jahn- Teller character
lifting the bare orbital degeneracy. Superconductivity in the d^4 and d^6
systems at variance with d^1, d^7, and d^9 systems implies an unavoidable
coexistence of the spin-triplet composite bosons and a magnetic lattice. We
argue that unconventional high-T_c superconductivity observed in quasi-2D
cuprates with tetragonally distorted CuO_6 octahedra and iron-based layered
pnictides/chalcogenides with tetrahedrally coordinated Fe^2+ ions can be a key
argument supporting the disproportionation scenario is at work in these
compounds.
