Jenn,
There is no way to change the spatial reference of the basemaps, however, you can make them reproject on the fly depending on the client you're using. For instance if you're using ArcMap, you define the coordinate system of the data frame and then when you add the basemap it will apply a geographic transformation on the fly. You'll receive a warning that the following data source uses a GCS that is different from the one used by the data frame.
Hope this helps,
- Daniel