How do I catch multiple exceptions and then pass them to specific handlers?

I have some code in a Java 8 app that throws N different exception classes which come from a separate library. There's currently a separate handler for each exception class despite them sharing some common code. I'd like to refactor this to avoid:

1. Repeating the list of exception classes that have some commonality (for example using a switch, instanceof or casting)
2. Repeating calls to someCommonCode N times

class MyClass {
  public void errorHandler(FirstException e) {
    System.out.println("This error is not so bad");
  }

  public void errorHandler(SecondException e) {
    System.out.println("This error is worse");
  }
  public void someMethod() {
    try {
      riskItAll();
    } catch(FirstException | SecondException e) {
      someCommonCode();
      errorHandler(e);
      moreCommonCode();
    } catch(Exception e) {
      uncommonCode();
    }
  }
}

So far, I've been stuck trying to find documentation / examples for dealing with multiple catch blocks in this way as I haven't found the term used to describe the type of e inside such a block. There's no searchable terminology introduced on http://www.oracle.com/technetwork/articles/java/java7exceptions-486908.html

It could be a generic, but that would be surprising since you can't catch an instance of a type parameter.

The code snippet above does not build - the compiler error raised at errorHandler is

error: no suitable method found for errorHandler(RuntimeException)
method MyClass.errorHandler(FirstException) is not applicable (argument mismatch; RuntimeException cannot be converted to FirstException)
method MyClass.errorHandler(SecondException) is not applicable (argument mismatch; RuntimeException cannot be converted to SecondException)