I’ve always found it helpful to think of \\ as a simple convenience rather than “default arguments.” All it’s doing is turning this:

def bar(a, b \\ 0) do
  a + b
end

into this:

def bar(a) do
  bar(a, 0)
end

def bar(a, b) do
  a + b
end

The easiest and clearest way to get what you want it to just write it out manually as suggested.

So the short answer is no, but technically yes if you consider redefining def and changing how \\ works

You can mix def and defp with different arities:

defmodule Foo do
  def bar(arg), do: bar(arg, 42)
  defp bar(arg, arg2), do: {arg, arg2}
end

iex(6)> Foo.bar(1)
{1, 42}

iex(7)> Foo.bar(1, 2)
** (UndefinedFunctionError) function Foo.bar/2 is undefined or private. Did you mean:

      * bar/1

    Foo.bar(1, 2)
    iex:7: (file)

I’d say yes. It’s just accidental that the private one happens to have a different arity, which allows for it being named the same.