Multi-gap RPC prototypes with readout on a multi-strip electrode were developed for the small polar angle region of the CBM-TOF subdetector, the most demanding zone in terms of granularity and counting rate. The prototypes are based on low resistivity ($sim$10$^{10}$ $Omega$cm) glass electrodes for performing in high counting rate environment. The strip width/pitch size was chosen such to fulfill the impedance matching with the front-end electronics and the granularity requirements of the innermost zone of the CBM-TOF wall. The in-beam tests using secondary particles produced in heavy ion collisions on a Pb target at SIS18 - GSI Darmstadt and SPS - CERN were focused on the performance of the prototype in conditions similar to the ones expected at SIS100/FAIR. An efficiency larger than 98% and a system time resolution in the order of 70~-~80~ps were obtained in high counting rate and high multiplicity environment.