The normal rule is you can apply manufactured weapons and natural attacks. The specific rule since were discussing a monk is they don't combine with flurry of blows.
There's a feat calles feralccombat training.
Flurry doesn't allow natural attacks to be added on since it already adds a bunch of good hits (I mean, it is basically TWF with all the hits getting double slice added on basically, and from what I understand a weapon that can be two handed such as a temple sword still gives 1.5x power attack).
Feral combat training allows you basically to treat a natural weapon like a monk weapon, getting the normal flurry attacks and bonuses on unarmed strikes on it. So the natural weapons do not do natural attacks, but they still get the benefits of things like rend or what have you. So it is usually specialized for really good natural attacks, and you might just want to go with boar style instead if you want to tear people apart with your bare hands (it's flavor is pretty much built around tooth and claw fighting).
But if you just mean whether you can mix unarmed strikes with natural attacks outside without flurry every coming up? Yeah, but unarmed strikes are considered manufactured weapons though, making all the natural attacks secondary (-5 to hit; 1/2 str and power attack bonuses). Again, not entirely optimal, but some people find ways to game such a build.