It's possible at super-minimal cost to have for the same document liquid AND fixed-width layout, thanks to ZE POWA of CSS...

In a fixed-width document named index.html, you usually have a rule setting the width or max-width of the main element. Something like

#main750 {
  max-width: 750px;
}

Right? Now think :target pseudo-class and tweak your style rule as followed:

#main750:target {
  max-width: 750px;
}

Do you understand the trick?

Yeah, your document now has liquid layout if called by URL index.html and fixed-width layout if called by index.html#main750 :-) TADA !