The Electron-Ion Collider (EIC) will use swap-out injection scheme for the Electron Storage Ring (ESR) to overcome limitations in polarization lifetime. However, the pursuit of highest luminosity with the required 28 nC electron bunches encounters stability challenges in the Rapid Cycling Synchrotron (RCS). One method is to inject multiple RCS bunches into a same ESR bucket. In this paper we perform simulation studies investigating proton emittance growth and electron emittance blowup in this injection scheme. Mitigation strategies are explored. These findings promise enhanced EIC stability and performance, shaping potential future operational improvements.
