Exceptional-point (EP) optics allows for innovative devices, such as a sensor based on a whispering-gallery-mode (WGM) microresonator. Meanwhile, WGM-enabled optomechanics has led to important advances, including optomechanically induced transparency (OMIT). The authors show that unconventional EP features can be observed in OMIT: Tuning the relative angle between two external nanoparticles coupled to the same microresonator causes EPs to emerge periodically, strongly modifying both the transmission rate and group delay of the signal, for a slow-light-to-fast-light switch. This approach is a means to engineer optomechanical EP devices for optical communication and signal processing.