Am I the only one that suspects there'd be a lot less confusion in mixed attack series and in feat functions if unarmed strike were its own category of attack type, instead of the weird fence-straddling it does between manufactured and natural weapon?
Well, it's only Monks who have the special "counts as both manufactured and natural" clause, and that's only for the purposes of spells or effects that enhance manufactured or natural weapons (letting them take INA, for example).
For everyone else, unarmed attacks are just a simple weapon. You can make off-hand attacks with them, even if your main-hand attacks are also unarmed strikes. Meanwhile, natural weapon users can gain iterative unarmed strikes (assuming they have IUS) while employing their natural weapons as secondary attacks. They can also do the TWF option, but the penalties are harsh without a whole pile of feats.