Is it possible to use the instanceof operator in a switch statement?

This is a typical scenario where subtype polymorphism helps. Do the following

interface I {
  void do();
}

class A implements I { void do() { doA() } ... }
class B implements I { void do() { doB() } ... }
class C implements I { void do() { doC() } ... }

Then you can simply call do() on this.

If you are not free to change A, B, and C, you could apply the visitor pattern to achieve the same.