Baron font only in italic, not regular

The 4 basic styles work as a family in word. It then requires a second family for the two black varieties.

What font with more than the 4 basic styles does work properly in word?

The best thing is to choose tools to suit the task. If sophisticated type-setting is an important requirement, InDesign, Quark, PageMaker, or PagePlus may be a better choice than Word.

If open sharing of work is most important, LibreOffice might be best.

This discussion has shown up the defects in Word for type-setting. You can do it, but with the limitations pointed out by Mike.

You could have a family of twelve type styles: with three font families Light, Medium, and Black, each with Regular, Italic, Bold, and Bold Italic styles. That would make it a little easier to use.

I found that Word handles a lot more fonts plain wrong. Reverting to Illustrator for design tasks involving type.

Yes, good choice–any vector design application or layout tool (but not MS Publisher) is a far better choice.