PHP: Dynamic or Programmatic Catch Blocks

I have a situation where it would be nice to be able to have a catch block where the type of the Exception is determined at run time. It would work something like this:

$someClassName = determineExceptionClass();

try {
  $attempt->something();
} catch ($someClassName $e) {
  echo 'Dynamic Exception';
} catch (Exception $e) {
  echo 'Default Exception';
}

Is this at all possible?