An apparatus allowing continuous acquisition of thickness measurements during electropolishing of superconducting cavities is described. The instrument is based on the ultrasound thickness measurement technique and allows the connection of up to six probes. The apparatus has been employed to monitor the surface treatment of PIP-II low beta single cell prototypes developed and manufactured by LASA-INFN and specifically to measure surface removal at different points of interest on the cavity surface. The apparatus facilitated the development and optimization of electropolishing parameters for incorporation into the cavity manufacturing process.