Abstract We discuss the possibility that the soft X-ray transient GRS 1915$+$105 evolved from a binary similar to V4641 Sgr (XTE J1819$-$254) by conservative mass-transfer, and estimate the possible mass-transfer rates during the evolution. The results indicate that the high mass-transfer rates could explain the high luminosities in ultraluminous X-ray sources. Although the high mass-transfer rates during evolution are accompanied by high luminosities, we find that much of the transferred matter may sweeps accompanying radiation in an adiabatic inflow of super-Eddington accretion. We suggest that soft X-ray transients with evolved companions (initial companion mass $ \gt 3 \,{{{M}_{\odot}}}$), e.g. GRS 1915$+$105, can be ultraluminous X-ray sources if they are seen through their beaming axis.