(defun mixed (arg1 &rest arguments &aux (arg2 30) arg2-supplied)
  (unless (member (first arguments) '(:arg3))
    (setf arg2 (pop arguments) arg2-supplied t))
  (destructuring-bind (&key (arg3 24 arg3-supplied)) arguments
    (list arg1 arg2 arg3 arg2-supplied arg3-supplied)))

(mixed 22 44)          --> (22 44 24 t nil)
(mixed 22 44 :arg3 33) --> (22 44 33 t t)