I made an interesting discovery.
I had run out of vodka and needed to make a Screw Driver with 1/8 vodka and 7/8 orange juice.
I did have cachaça and used it instead, figuring that if you could use vodka in place of cachaça in batida (caipirinha -> caipirovska) why not use cachaça in place of vodka in a screw driver.
Wotta surprise! It was much smoother and fruitier than a normal screw driver, and it had a mellower fruity taste than a caipirinha.
I call it Cachave de Parafusos as a combination of Cachaça and Chave de Parafusos.
One thing though, it must be North American style orange juice, which is more of a nectar than a juice. It seems that the orange juices in other parts of the world are too watery to produce the right fruity effect. The sad thing is that the orange juices in the rest of the world are more natural.