We demonstrate the potential of all-optical switches in integrated waveguides based on intermodal cross-phase modulation between transverse modes. For this purpose, the differential phase between two transverse modes of a probe beam was altered by cross-phase modulation with a control beam propagating only in the fundamental mode. A switching behavior was accomplished by spatially filtering the resulting multimode interference of the probe modes, which changed depending on the control beam power. All-optical switching with a contrast of 82% at 1280 nm over a frequency range of 4.4 THz at 1.6 nJ was achieved, representing an improvement of the product of necessary power and waveguide length by a factor of nearly 2000 compared to similar experiments in graded-index fibers. Additionally, we show that the center wavelength of the switch can be tailored by changing the cross-sectional geometry of the waveguide or the involved probe modes.