That's only the syntax of s-expressions - a data format.

The Lisp syntax is defined on top of s-expressions.

For example Common Lisp has a CASE operator. That's the EBNF syntax:

    case keyform {normal-clause}* [otherwise-clause] => result*
    normal-clause::= (keys form*) 
    otherwise-clause::= ({otherwise | t} form*) 

An example:

    (case id
      (10 (foo))
      (20 (foo) (bar))
      (otherwise (baz)))

The expressions are written using s-expressions as data. But still there is structure in those s-expressions, described by the EBNF syntax of CASE.

Every special operator and every macro provides syntax. Since users can write macros themselves, everybody can extend the syntax. On top of s-expressions.

That is interesting. I've always considered lisp in terms of denotational semantics. In fact, I wrote a toy lisp in which the complete grammar was basically

    list -> ({symbol | number | string | list}*)

and then it was up to the interpreter to decide the meaning of special forms. (I say "basically" because there was also desugaring of '(...) to (quote ...)).