It is certainly possible to build a treehouse in a palm tree, or even have it spread over many trees, though the design must necessarily vary from what many people traditionally associate with treehouses. Palm trees actually have a few advantages sometimes overlooked. For example, the trunks of most other types of trees are composed primarily of dead wood, with the living part of the tree a narrow band just under the bark. This makes it easier for the entire tree to be damaged. Palm trunks, on the other hand, are composed entirely of living material.
The usual vision of a tree house is that of a wooden platform wedged high among the outstretched branches of a sturdy oak or maple. The obvious design differences make that impossible with a palm tree, which has no sturdy, sweeping branches among which to nest a treehouse. With a palm, the trunk is sturdy enough to support weight, but there simply are no branches available for the project. However, treehouse architects have figured out a workaround solution.
To build a treehouse in a single palm tree requires that the design be constructed as a platform encircling the trunk at the preferred height. In the absence of branches to support the structure's weight, the entire house should be attached to the trunk by other means of support, usually beams nailed to the bottom of the treehouse and then to the palm tree. A stronger and more elaborate style of treehouse could be built among a palm grove, with the trunks of several trees serving as the foundation. Treehouse design company Playa Viva shows examples on its website.
There is a basic difference between the roots of a palm tree and those of other species. Most trees have a root system built of individual roots that are thick near the surface of the earth and taper to smaller points as they grow down. Palm tree roots are the same thickness from the surface to the most distant tip, which essentially allows it to take a firmer grip in the earth, providing a perfectly suitable platform upon which to build a treehouse.
Whether building a treehouse in a palm tree simply so the kids have a place to play, or to have an actual house with running water and electricity, rest assured it can and has already been done. Treehouse construction expert Micheal Garnier has made a career of building treehouses in a variety of tree types. When it comes to palms, keep in mind that you can transplant trees into the exact location you need, though make sure you live in a climate that stays warm enough for them to flourish.