As the title says, I find it useful to be able to overload operators.  Is it possible to also change the way the operators are parsed by specifying the precedence and associativity of overridden operators?
Can I change operator precedence and associativity in C++?
c++;operators
No, you can't do that and that's a good thing. Operator overloading already has enough potential to make code unreadable without being able to change precedence or associativity.If you even want to do that you are probably abusing operator overloading and should use normal functions instead.