Empiricism has 7 dogma rather than just 2. These are:
1) Mind is a tablua rasa (blank slate)- nurture over nature.
2) True knowledge must be testable.
3) Unobservables cannot give true knowledge- kinda follows from 2.
4) Science aims to find laws or patterns in the world.
5) Science should follow the "covering law model" which means that the laws are literal reflections of the world out there.
6) The laws that science finds should work both ways. If a law is accurate, it should be able to explain stuff that's happened in the past AND be useful for predicting stuff in the future. This follows from 5.
7) Science should be free of subjective values and beliefs.
Empiricism is not something that destroys positivism. Rather, empiricism is a key part of positivism.
I would say that in a way empiricism, through finding things like "unobservables" with the help of specialised instruments (eg atomic structures are only visible through the use of things like electron microscopes), ends up tripping itself up which is why I think most scientists today take a kinda "neo-positivist approach"- empiricism without the dogmatism and a focus on reflexivity (revising theories as you go), considering science as fallible (we might never find the "final" answer).
Another example of things science has discovered that go against the dogma is Chomsky's universal grammar and "language acquisition device" which means that the capacity for language is innate/instinctual- this goes against the idea of the tabula rasa. Also, we can't say that science will be free of subjective values and beliefs because language is never perfect, as shown by Wittgenstein- people can interpret the same thing in different ways. Feminist approaches to science have also pointed out that positivism focuses on the object of research without really considering how science is a socially constructed phenomena.