Beam acceleration in the International Linear Collider (ILC) will be provided by 9-cell 1300 MHz superconducting (SC) cavities. The cavities are designed for effective acceleration of charged particles moving with the speed of light and are operated on π-mode to provide a maximum accelerating gradient. A significant research and development effort has been devoted to develop ILC SC technology and its rf system which resulted in excellent performance of ILC cavities. Therefore, the proposed 8-GeV proton driver in Fermilab is based on ILC cavities above ∼1.2 GeV. The efficiency of proton beam acceleration by ILC cavities drops fast for lower velocities and it was proposed to develop squeezed ILC-type (S-ILC) cavities operating at 1300 MHz and designed for β_{G}=0.81, geometrical beta, to accelerate protons or H^{-} from ∼420 MeV to 1.2 GeV. This paper discusses the possibility of avoiding the development of new β_{G}=0.81 cavities by operating ILC cavities on 8/9π-mode of standing wave oscillations.