There are definite advantages in using more than one tree for your treehouse - the treehouse can be bigger, and you have to use less bracing. The tree(s) you see here (behind the magnolia!) are a very tightly grown group of three trunks - they all touch at the base, and splay out somewhat as they grow upwards. At the height of the treehouse - about 9 ft (2.7 m) off the ground - one pair of trunks are still almost touching, and the other one is about 4 ft (1.2 m) away. This means the design has been based on one for a close-spaced pair of trees, rather than for a group of three. The trees are Garry oaks, and they don't grow much further north than this (southern Vancouver Island), so they grow pretty slow here. A solid gnarly collection of old trees, each about 1 ft in diameter at 9 ft up.
Start by figuring out how high you want the treehouse. 9 feet is exciting for kids but not scary. You can of course go higher, but you'll have to take more account of movement.