I have a distinct feeling that there's some apparent no-go on the question in the title, but currently can't put my finger on it;
For the lifting mass to Low Earth Orbit (LEO), let's assume that SLS (Space Launch System) Block 1 is completed (crew and cargo) and for payload size that the missions could use ESA's ATV-derived Orion Service Module. Obviously, Orion Crew Module would be used with the maximum crew size of four, where the HST-STS missions had a crew of seven. Let's say that we need to launch at least as numerous crew as the number of Extravehicular Activity (EVA) astronauts during each HST-STS mission. All other mission parameters would stay identical to the "4½" (OK, 5) Hubble Space Shuttle servicing missions (STS-61, STS-82, STS-103 + STS-109, STS-125).
So could Orion eventually pull something like this off, even if multiple launches are used for each individual mission?