Offset printing can have more colors than CYMK. Sometimes a setup will include multiple additional inks beyond CYMK to produce a color or effect that CYMK alone can't produce. Sometimes those colors will be mixed from other colors as well much like paint.

Problem is offset printing presses are HUGE and expensive and require making plates first. There are digital offset presses, but they generally can't have an other stage added like traditional offset printing, it's capped at however many colors that machine has built in. They also are huge compared to other printers people will have at home or the office.

-EDIT- It is probably possible to scale down the hardware and do something like digital offset presses. I think it would cool if there was a *small* printer people could connect multiple color stages like a legos and mix up a colors for those stages.