Anarchy, Monarchy and Republic can exist together. In fact it is system which was practiced in Poland in the end of XVII and whole XVIII century. And the law in such system might be stronger than anything else, for example so called "golden freedom's" in Poland that time.
As for monarchy it can exist together with democracy, just like in United Kingdom. The main rule in democracy is equality in the face of law. Monarchy doesnt violate this rule because monarch and his/her familly are not citisens who have better rights than other citisens but they are rather some kind of institution (for sure monarch, its harder to say it about his familly).