Another in a long list of Mills Mess tricks which borrow a little extra something from another trick, in this case we're borrowing from The Spiral.
If you learnt Mills Mess using The Spiral Way I can guarantee that you can already do this trick. But if you didn't, it's not a problem, this description only assumes that you can juggle Mills Mess. In the Spiral way of learning Mills Mess, you practised changing from clockwise & anticlockwise Spirals, then gradually reduced the number of throws between each direction change until you were switching on every third throw. Now we're going to INCREASE the number of throws between each switch.
Juggle a standard Mills Mess & count out the throws starting with the underarm throw as 1, carry on juggling for a while & count to yourself, "1, 2, 3, 1, 2, 3..." just to get the feel of the rhythm. Now you are going to add on two throws of a Spiral on one side.
The next two paragraphs may be a bit tricky to follow so you might like to read it without holding any balls & mime the motions along the way.
When it comes to making an Under the arm throw, DON'T throw it straight up so that it falls back down to the point it was thrown from. Instead reach under & throw from the opposite side of the body so that it follows the path of the ball that was thrown immediately before it. That is if you are throwing from the left underneath the right arm you will reach under to the right hand side of the body & throw the ball so that it will land on the left hand side of the body.
After making the under arm throw, quickly uncross your arms. The arm that was on top carries its ball back underneath the ball thrown under the arm, then throws an Over the top throw which directly follows the path of the previous under arm throw. The arm that was on the bottom catches the ball that was immediately following the ball caught by the upper arm & carries it under the opposite arm for an under arm throw. Throw this one straight up & go back into Mills Mess. Phew.
Practise that move on both sides until solid. Then just add on the two extra Spiral throws every time that you would normally throw a ball under the arm. The full pattern has five beats, so you can count out, "1, 2, 3, 4, 5, 1, 2, 3, 4, 5.." where the ones are the straight up underarm throws. That's all there is to it.