Not exactly like in Shogun II, no.

Like the previous few games, every army needs a general. The big innovation is that, now, generals are much more common. Each general can command up to six units and each army can have up to three generals, for a full stack of 21.
So when you ask if you can split up armies... Kind of. You can split them depending on how many units each general has. For example, if you have an army with a general with 3 units, a general with 5, and a general with 1, you can split off the general with just one unit, or the one with just two or split off all three into three different armies with different sizes.