As of this writing, only the Gardening Shed and Music Amphitheater are available to upgrade, but additional buildings will be added to this list over time. In the case of the Gardening Shed, as an example, you can upgrade the building up to Level 6, collecting building materials for each upgrade. For the first upgrade, you'll need two Gloves, two Stones, two Hard Hats and a Guardian Seal, with items being earned by simply asking your friends to send them to you.
Each upgrade level of the Gardening Shed will see the building change shape and appearance, and will see the building offering more Estate Points in the process. For instance, a Level 3 Gardening Shed will offer 368 Estate Points, which is higher than the original allotment of 320 Estate Points. Is that a lot of work for a little return? Perhaps, but when land space is that much of an issue for some players, any additional points are better than nothing.
As one final note, those players that have purchased a Pegasus Fountain can continue to use the fountain to receive building parts, but these will only be parts for first-run buildings, and not those that you're upgrading. Good luck!
What do you think of these building upgrades in Hidden Chronicles? Have you already started upgrading your Gardening Shed or Music Amphitheater? Sound off in the comments!