Only way to add new fields and process those fields is CB Auto Actions or a custom plugin. onAfterEmailUserForm can be used to add new fields to the form the same way CB AntiSpam does with captcha. onBeforeEmailUser can then be used to process those fields and add that information to the email. Both triggers variables are as follows.
onAfterEmailUserForm
Code:
$_PLUGINS->trigger( 'onAfterEmailUserForm', array( &$rowFrom, &$rowTo, &$warning, 1, &$allowPublic, &$name, &$email, &$subject, &$message ) );
onBeforeEmailUser
Code:
$_PLUGINS->trigger( 'onBeforeEmailUser', array( &$rowFrom, &$rowTo, 1, &$emailName, &$emailAddress, &$subject, &$message ) );
Most variables are references so for example you can modify the message of the email and add the fields to it. There is no functionality to add BCC/CC/Attachments from this trigger though if that's what you're needing.