By default natural weapons do not allow iteratives. The monk's unarmed strike already breaks that. The only indication that you might be unable to pick up multi- or two-weapon fighting with the monk is this line:
There is no such thing as an off-hand
attack for a monk striking unarmed. A monk may
thus apply her full Strength bonus on damage rolls
for all her unarmed strikes.
However, inserted in the context of the ability's entry, it seems to be there only to explain the presence of the next line.
That's the stupidest thing Wizard has ever printed. That's worse then letting Pun Pun slip through the cracks. That
one line has been debated since print. I think my explanation is the intent, but RAW? It honestly doesn't make sense. It's especially silly when in the FAQ it is stated that you can take TWF to allow for more attacks. But that begs the question, how? Due to how IUS is written, it'd be like taking TWF to make offhand attacks with a two handed weapon. If IUS is a special type of natural attack that allows iterative attacks, that makes sense. But if it allows TWF, that implies there
is an offhand, because that's why TWF does, lowers penalties on offhand strikes. Therefore, if you can make offhand attacks, whats to stop you from taking Multi-weapon fighting? ...nothing. You're right. If there is an offhand attack option for IUS, there are infinite attack options for IUS.