  Recent observation of pressure induced second superconducting phase in
AyFe2-xSe2 [A=K, (Tl,Rb)] calls for the models of superconductivity that are
rich enough to allow for multiple superconducting phases. We propose the model
where pressure induced changes in Fermi surface topology lead to appearance of
the hole pocket at $\Gamma$ point at high pressure. We develop low-energy
effective model, derived from first-principles band-structure calculation, to
suggest the phase assignment where low pressure superconducting state with no
hole pocket at $\Gamma$ point is a nodeless d-wave state. It evolves into a s+-
state at higher pressure when the Fermi surface topology changes and hole
pocket appears. We analyze the pairing interactions using five band tight
binding fitted band structure and find strong pairing strength dependents on
pressure. We also evaluate the energy and momentum dependence of neutron spin
resonances in each of the phases as verifiable predictions of our proposal.
