Here is how i think it runs (havnt run a game yet). Suppose we have two Kai Lords, Swift Fox (CS 17, EP 24) and Rune Dancer (CS 15, EP 27) against 3 Mountain Giaks (all CS 12, EP 14)
Round 1
Swift Fox has the higher CS, so rushes in to attack Mountain Giak 1 and Mountain Giak 2, since he is feeling brave. Swift Fox is now considered to be engage with two enemies, so he makes his first attack against Giak 1 (CR +5) and rolls a 0, inflicting 18 EP, killing it in one blow! Then he makes a second attack against Giak 2, who gets +2 CS because swift fox is engaged with one other enemy. This time he rolls a 5, which at CR +3, inflicts 9 EP, but he loses 2 EP (now down to 22).
Next Rune Dancer has a turn to act and so attacks Giak 3. With a CR of +3, she picks a 1, so inflicts 6 EP, but takes 3 EP (now reduced to 24).
Round 2
Now just 2 Giaks remain, 2 (EP 5 ) and 3 (EP 8 ). Swift Fox decides to attack 2 again, and can also reach Giak 3, who is engaged with Rune Dancer. His first attack is made at Giak 2, is made at CR 5 - he picks a 7, and inflicts 12 EP killing it out right. His second attack is made at CR +3, because this is the second enemy he is engaged with. unluckily, he picks a
1, so only inflicts 5 EP (Giak 3 now only has 3 EP though) but takes 4 EP himself (reduced to 18 EP).
Now Rune Dancer makes an attack, and since his enemy is also engaged with Swift Fox, may add +2 CS, so at CR +5 picks a 3, killing the Giak, but taking 3 EP in the process.