An advanced Electron Beam Ion Source (EBIS) is the primary ion source to supply highly charged ion beams of different elements to the Relativistic Heavy Ion Collider (RHIC) and to the NASA Space Radiation Laboratory (NSRL). Intense beams of highly charged ions of various elements of the periodic table, ranging from helium to uranium, have been demonstrated since EBIS became operational in 2010. EBIS routinely provides ion beams to RHIC and NSRL quasisimultaneously with about 1 s switching time between different ion species. Such unique flexibility and rapid switching between ion species are based on external injection of singly charged ions into the EBIS trap either in "fast" or "slow" injection modes. At present, a Laser Ion Source (LIS) provides most of the ion species of solid materials using the "fast" injection mode into the EBIS trap and a Hollow Cathode Ion Source (HCIS) provides most of the ion species of gaseous elements using the "slow" injection mode into the EBIS trap. Gas injection into the EBIS trap is also possible and has been used but imposes some restrictions for the simultaneous generation of highly charged ions such as Au32+ ions for RHIC and ions of gaseous species for NSRL. Because light ions have relatively high velocity inside the EBIS trap, efficient injection of hydrogen and helium ions and filling of the EBIS trap to high capacity is difficult from either LIS or HCIS. To overcome this restriction and enhance EBIS operational capability, we suggest injecting beams of hydrogen and helium cluster ions into the EBIS trap. Required parameters of cluster ion beam injection into the EBIS trap are estimated, and advantages of such an injection are highlighted. A cluster ion source with required high intensity is visible and will be designed, built, optimized, and tested.