 A few have more than one because they are 
groups of Lie type in more than one way.For symmetric groups (and other Coxeter groups) the sign representation is analogous to the Steinberg representation.Some of the sporadic simple groups act as doubly transitive permutation groups so have a BN-pair for which one can define a Steinberg representation, but for most of the sporadic groups there is no known analogue of it.