Can I catch multiple Java exceptions in the same catch clause?

This has been possible since Java 7. The syntax for a multi-catch block is:

try { 
  ...
} catch (IllegalArgumentException | SecurityException | IllegalAccessException |
            NoSuchFieldException e) { 
  someCode();
}

Remember, though, that if all the exceptions belong to the same class hierarchy, you can simply catch that base exception type.

Also note that you cannot catch both ExceptionA and ExceptionB in the same block if ExceptionB is inherited, either directly or indirectly, from ExceptionA. The compiler will complain:

Alternatives in a multi-catch statement cannot be related by subclassing
  Alternative ExceptionB is a subclass of alternative ExceptionA

The fix for this is to only include the ancestor exception in the exception list, as it will also catch exceptions of the descendant type.