Basically, if you highlighted it and changed the color to, say, red, only parts of glyphs would turn red - the rest would stay black no matter what.
The font standards are a bit limited here. Currently it is possible to only have either solid 1 color fonts or OTF SVG (icon) color fonts that have a fixed color from the font file. There is no mechanism in the current standard to parametrize color. It is definitely an oversight.
But there is a workaround. Before it was possible to do SVG fonts and after the most free form postscript variants were deprecated there was still a niche for colored fonts. So what they do is they split the font into two. one for the background and one for the decoration. Then all you do is type the text on top of itself one with the base font and one with color decoration. And presto you can adjust the color. No rainbows though.
I'm sure if this were possible, such fonts would already exists - especially for more decorative fonts designed for use in sign making and things of that nature.
I've never seen such a font.
I don't think it's possible as live type. But, as with all things, I could be wrong.
Of course, converting type to outlines would allow one to color only a portion of a glyph - but then it becomes shapes and is no longer "type".