I'm not sure where you're seeing that limit.
In QGIS 2.18 at least, you have access to all Unicode characters which your font supports. They should also appear in the selection of the Font Marker style.
Here's an example, zoomed in so you can see. I've got a layer of around 30000 grid squares, each with a unique id (field
If I use labels with this expression...
you can see a lot of unicode characters...
Here, I used the font 'unifont'. It's a bitmap font, which is why it's blocky, but also got it work with other traditional fonts which have good unicode coverage.
Your mileage will vary according to the font you're using; some fonts (particularly decorative ones) may be limited to ascii/latin characters, as MaryBeth pointed out.