For decades since the development of phase-contrast optical microscopy, an analogous approach has been sought for maximizing the image contrast of weakly-scattering objects in transmission electron microscopy (TEM). The recent development of the laser phase plate (LPP) has demonstrated that an amplified, focused laser standing wave provides stable, tunable phase shift to the high-energy electron beam, achieving phase-contrast TEM. Building on proof-of-concept experimental demonstrations, this paper explores design improvements tailored to biological imaging. In particular, we introduce the approach of crossed laser phase plates (XLPP): two laser standing waves intersecting in the diffraction plane of the TEM, rather than a single beam as in the current LPP. We provide a theoretical model for the XLPP inside the microscope and use simulations to quantify its effect on image formation. We find that the XLPP increases information transfer at low spatial frequencies while also suppressing the ghost images formed by Kapitza-Dirac diffraction of the electron beam by the laser beam. We also demonstrate a simple acquisition scheme, enabled by the XLPP, which dramatically suppresses unwanted diffraction effects. The results of this study chart the course for future developments of LPP hardware.