Real-time estimation of cosmic-ray fluxes on satellite orbits is one of the greatest challenges in space weather research. Therefore, we develop a system for nowcasting and forecasting the galactic cosmic ray (GCR) and solar energetic particle (SEP) fluxes at any location in the magnetosphere and ionosphere during ground-level enhancement (GLE) events. It is an extended version of the WArning System for AVIation Exposure to SEP (WASAVIES), which can determine event profiles by using real-time data of the count rates of several neutron monitors (NMs) at the ground level and high-energy proton fluxes observed by Geostationary Operational Environmental Satellites (GOES) satellites. The extended version, called WASAVIES-EO, can calculate the GCR and SEP fluxes outside a satellite based on its two-line element (TLE) data. Moreover, organ absorbed-dose and dose-equivalent rates of astronauts in the International Space Station (ISS) can be estimated using the system, considering its shielding effect. The accuracy of WASAVIES-EO was validated based on the dose rates measured in ISS, as well as based on high-energy proton fluxes observed by POES satellites during large GLEs that have occurred in the 21st century. Agreement between the nowcast and forecast dose rates in ISS, especially in terms of their temporal structures, indicates the usefulness of the developed system for future mission operations.