Each general can only inspire one unit at a time, since the duration of the ability is much shorter than the cooldown. The AI however tends to bring several generals in a single fight, which is probably why you encounter armies with more than one inspired unit at once.
The only way I'm aware of to inspire more than a single unit is to bring more generals into the fight. Sadly, when a battle is over, only the general leading the army gains experience, so it is inefficient to simply get them all into a single stack. If you spread them into separate armies before the battle and have them enter as backup, all of your generals will gain experience. The backup armies don't need to have any subordinate units, the general by himself enough. To do that, just move all generals in a single army and when you're about to attack, separate the generals and place them on the edge of the enemy's aggression bubble, then assault with the main army, led by a single general with the highest command or most useful attributes. The end goal is to have all of the generals entering the battle, with none of them being in an army with another general in it. You can also have your secondary generals travel separately from the army, this way they'll work as forward scouts due to being faster. If lucky, they may also trigger an ambush, which they have a good chance of surviving thanks to their speed (especially if your battles have a time limit), unlike your main army.