The pressure effect on the superconducting transitions in La2-xSrxCuO4+delta is investigated by ac susceptibility measurements up to 2 GPa. Two series of samples with x=0 and x=0.015 and 0<delta<0.11 are compared with respect to the ambient and high pressure properties. At ambient pressure both sets of samples fit into the same phase diagram as a function of the total hole concentration (Sr- and oxygen doping contribute to the total carrier density, p). A single superconducting transition (T(c)approximate to30 K) for p<0.085 splits into two transitions (T(c)approximate to15 K and 30 K) at higher hole density indicating that electronic phase separation sets in above p=0.085. The pressure effect on T-c of the 3 0 K transition is unusually large, dT(c)((30))/dPapproximate to10 K/GPa. The electronic phase separation at higher hole density is enhanced by pressure and T-c of the 15 K superconducting state exhibits a negative Pressure shift, dT(c)((15))/dPapproximate to-4 K/GPa. At a hole density close to 0.085 the electronic phase separation into the two superconducting states can be induced by pressure. The results are interpreted in terms of a strong correlation of the hole system and the interstitial (mobile) oxygen ions. Pressure, applied at ambient temperature, causes a redistribution of holes and oxygen and enhances superconductivity (T-c) as well as the tendency to phase separation.