There is now a CSS Nesting Module in the CSS specification. The module is currently a Working Draft and CSS nesting is supported in all major browsers.

The syntax looks like this:

table.colortable {
  & td {
    text-align:center;
    &.c { text-transform:uppercase }
    &:first-child, &:first-child + td { border:1px solid black }
  }
  & th {
    text-align:center;
    background:black;
    color:white;
  }
}

.foo {
  color: red;
  @nest & > .bar {
    color: blue;
  }
}

.foo {
  color: red;
  @nest .parent & {
    color: blue;
  }
}

:not() only accepts one simple selector at a time; this is mentioned in the Selectors 3 spec:

The negation pseudo-class, :not(X), is a functional notation taking a simple selector (excluding the negation pseudo-class itself) as an argument. It represents an element that is not represented by its argument.

The simple selectors in your example would be the two div tokens that you have. Other simple selectors include class selectors, ID selectors, attribute selectors and pseudo-classes. It does not accept more than one simple selector, nor does it accept combinators like > or space.

Depending on which elements you're trying to select exactly, there may not be a way to exclude div > div:

• If you only want to select elements that are children of a div, that are themselves not div, use this instead:

  div > :not(div)
  

• If you only want to select div elements whose parent element is not a div, use this instead:

  :not(div) > div
  

If you want to use this negation by itself, selecting all other elements, then there isn't a way using just a selector.

The only other viable workaround in CSS that I can think of is to apply styles to the elements you want without the :not() expression, then undo them for div > div. This works for any set of elements you're trying to target; the disadvantage is that not all properties can be easily reset.

Alternatively, if you're using jQuery, which does support :not(div > div) unlike the CSS version, you can place the selector in a script and, for instance, have jQuery apply a class name to those elements then target that class in your CSS.

Oh - nesting cannot be done

The :has() pseudo-class cannot be nested within another :has().

https://developer.mozilla.org/en-US/docs/Web/CSS/:has

#outer-div:has(> .inner-div + .inner-div) works to select "a parent with a child who is a sibling" which is sufficient

Both are completely acceptable to use and the answer depends on your specific solution. For instance if you have other areas where you are sharing common properties that are defined by that class you'd want to keep it as general as possible. If for instance you have a navigation and the links in that area share some common elements those could be defined by a.link

Then in your nested html, you might do something like

.someclass a.link {font-size:8px} to make that text smaller.

Here is an article that discusses how the specificity works: http://coding.smashingmagazine.com/2007/07/27/css-specificity-things-you-should-know/