The cover and fend/Crazy Monkey:

The position for the cover and fend is made by placing both palms on the crown of your head, leaving your forearms and elbows covering your face and chin. This position is never static but constantly moving and covering the entire head/facial area just like an exaggerated motion of washing your hair, as you slip your body and move your head to the left and right, to present a harder to hit moving target.

The hands constantly move to protect the head and face from a multiple punching attack. The front of your forearms and elbows deal with any frontal straight punch, while the sides of either outer arm can be closed tight to cover any angular (hook line) punches from the side. In reality you want to close him down after one or two punches are taken on the arms; and finish it from the clinch. This method combines CQB instructor Simon Squire's method of using the Fend; along with the Crazy Monkey concept from MMA coach the excellent Rodney King

 

Additional note:

A good way to practice is to have a partner wearing boxing gloves, throw multiple punches at your head as you stand with your back to a wall. It is important to only go forward as you cover and fend, moving back gives your opponent room to operate and develop power. So by training with your back to the wall, the only way you can go is forward. Practice the drill for say 20 seconds then close him down into a clinch. This will help you to develop composure to deal with this kind of multiple punching attack. In reality go for the close down as soon as the attack starts whether we are fending multiple punches from a skilled boxer or a wind milling Neanderthal the response is the same. Cover your head with your hands and arms, presenting your opponent with only the points of your elbows and forearms to hit and drive forward to close him down as soon as the assault starts.

As the aggressor throws punches strive to destroy his fists with your pointed elbows as you dive through his space and guard and clinch onto his neck.

From here get inside to clinch the neck and finish with multiple knees to the groin and thighs; follow up as appropriate.