  We study the two-dimensional Kondo lattice model with an additional
Heisenberg exchange between localized spins. In a first step we use mean-field
theory with two order parameters. The first order parameter is a complex
pairing amplitude between conduction electrons and localized spins which
describes condensation of Kondo (or Zhang-Rice) singlets. A nonvanishing value
implies that the localized spins contribute to the Fermi surface volume. The
second order parameter describes singlet-pairing between the localized spins
and competes with the Kondo-pairing order parameter. Reduction of the carrier
density in the conduction band reduces the energy gain due to the formation of
the large Fermi surface and induces a phase transition to a state with strong
singlet correlations between the localized spins and a Fermi surface which
comprises only the conduction electrons. The model thus shows a doping-driven
change of its Fermi surface volume. At intermediate doping and low temperature
there is a phase where both order parameters coexist, which has a gapped large
Fermi surface and d-wave superconductivity. The theory thus qualitatively
reproduces the phase diagram of cuprate superconductors. In the second part of
the paper we show how the two phases with different Fermi surface volume emerge
in a strong coupling theory applicable in limit of large Kondo exchange. The
large-Fermi-surface phase corresponds to a `vacuum' of localized Kondo singlets
with uniform phase and the quasiparticles are spin-1/2 charge fluctuations
around this fully paired state. In the small-Fermi-surface phase the
quasiparticles correspond to propagating Kondo-singlets or triplets whereby the
phase of a given Kondo-singlet corresponds to its momentum. In this picture a
phase transition occurs for low filling of the conduction band as well.
