That’s basically what is done all the time in languages where monkey patching is accepted as idiomatic, notably Ruby. Ruby is not known for its speed-first mindset though.

On the other side, having a type holding a closed set of applicable functions is somehow questioning.

There are languages out there that allows to define arbitrary functions and then use them as a methods with dot notation on any variable matching the type of the first argument, including Nim (with macros), Scala (with implicit classes and type classes), Kotlin (with extension functions) and Rust (with traits).