Date format suffixes

Is there a way to do date suffixes with ICU formatting? A lowercase d prints the day with no leading zeroes, but can you also add rd, th, st depending on the day, like April 14th?

I couldn't find anything in the documentation for that.

Not sure if this is what you're after, but this was helpful last time I was wrestling with date formats:

A bit of a tangent, but I also think this might be useful if you're into natural language syntax and want to tweak the output format:

Not with ICU formatting, I believe, but in the Fancy Ordinal Date Formatting discussion you'll find an elaborate macro that offers just that.

That looks like exactly what I'm after. Thanks!