I'm interested in the question in the title.

Does a spherical building $B$ always embeds in a building $\tilde B$ of type $A_n$ for some $n$?

By embedding I mean an isometric embedding with respect to their $CAT(1)$ metric. If the question has a positive answer, then how does this embedding works? For instance, does an automorphism of $B$ extends to an automorphism of $\tilde B$?

Edit: I forgot, that there are strange polygons. I would like to restrict the question to the case of irreducible thick buildings of rank at least 3. In particular, they are Moufang.