I doubt it is possible to do that now since the Chromebook is still new and I believe the harddrive in them are different from your typical laptop harddrive. Give it some time and a Chromebook manufacture such as Samsung or Acer might released chromebook harddrive upgrades.
For now I guess you can store whatever you can in the clouds or try to use an external harddrive. Western Digital makes some really good externals.
They are SSD's You can upgrade it but just depends on what kinda of SSD the Chromebook used last time i checked the Chromebook SSD is connected to an Msata cable, it all up to you but what i would do is just use an external