(defun mixed (arg1 &rest arguments &aux (arg3 24) arg3-supplied (arg2 30) arg2-supplied)
  (loop :while arguments
        :do (case (first arguments)
              (:arg3
               (pop arguments)
               (unless arguments (error "Missing argument after :arg3"))
               (setf arg3 (pop arguments) arg3-supplied t))
              (otherwise
               (cond
                 ((not arg2-supplied) (setf arg2 (pop arguments) arg2-supplied t))
                 (t (error "Too many arguments, remaining: ~S" 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)