all the things, if macro system is sufficiently sophisticated (ie., hygienic with ability to attach metadata to syntax object). Racket is one of languages with such system, and they implemented static typing using them.
Racket's define-syntax/syntax-parse has escape hatches into procedural generation (through which you can easily break the hygiene), and the equivalent of CL's &environment contains more information and allows more operations in Racket. Racket also supports reader extensions but often doesn't need them because it has a macro-based API for module definitions (a feature completely absent from, or even alien to, Common Lisp; OTOH, Elixir borrows some of Racket's ideas in this space).
For a practical example, Coalton and Typed Racket implementations show that both systems are capable of large-scale language extensions. I never studied their respective codebases, so I can't say anything about relative ease of introducing those extensions, but they are possible in both cases, at least.
What Let Over Lambda calls limited power, is probably in reference narrowly to `syntax-rules`. It's not just that it's hygienic, but that it purposefully has no way to opt out of it (unhygienic capabilities in a hygienic system are trivial to provide; but they still need to be provided by language implementation) but what's even more limiting is that it doesn't let you write procedural macros, it's all arcane pattern matching and templates. `syntax-case` (part of r6rs) doesn't have these issues.