I've seen plenty of designs for one & two story timber-framed homes. Other than a steep-pitched roof (which creates a tall attic space,) I've not seen a three-story design.

What's different? What additional factors are there to consider? Is it possible to take a two-story design and stretch it to three?

Plenty of the barn designs that I've seen use tall (25 plus foot) posts.

Three-story (and higher) timber frames appear to be common in Europe, especially in urban areas where building up makes more sense than building out.

The difference is that these multi-story buildings do not use continuous vertical posts that span multiple stories, instead the posts only span a single story. The frames are built up one story at a time, as if stacked in layers.

Some multi-story frames have cantilevered or jettied upper stories that go out as they go up, whereas other frames simply go straight up.

One consideration would be what type of enclosure system was planned, and if the horizontal frame members were green or dry, because of cross grain shrinkage issues.

Stretching a 2 story frame design to 3 stories using longer posts may be possible, however one would need engineering verification that the number of posts and their locations, the post cross sections, the bracing/sheathing system, and the foundation system would be adequate for the increased loads.