Unless they release a different xbox one version with this in mind then this suggestion isn't something that can be patched via software. The One wasn't designed for the drive to be easily removed like on the PS4.
I'm real disappointed in Microsoft for the major short sightedness they showed in the hardware for this generation. Mediocre RAM and a 250 gig hard drive is pathetic, especially since Microsoft really wants to push digital only content. I mean talk about anti-future proof, the One most likely won't make it 1 year before there is enough titles for it to fill the stock hard drive. I mean you're telling me for $500 for the console and $50 for live they couldn't have sprung for a 2 TB drive, especially with games taking up between 5 - 15 gb average size a pop? I realize Microsoft wanted to actually make a profit from the One unlike the original xbox (and 360 which broke even) but it's only hurting Microsoft's end goal of going digital only if people can't fucking install more than a handful of games at any one time. It took a massive amounts complaints to even get them to add in a graphic which tells you how much space is left on your device.
Regarding the proprietary harddrive joke someone made earlier, it's funny to think that the original 360 had an easily removable harddrive on the outside of the device. While I would prefer an easily accessible standard harddrive like the PS4 has, I wouldn't be strictly against proprietary either if there were multiple capacities to choose from and were competitively priced.