(a) The parties to the action or proceeding may stipulate to reclassification of the case within the time allowed to respond to the initial pleading.
(b) If the stipulation for reclassification changes the jurisdictional classification of the case from limited to unlimited, the reclassification fee provided in Section 403.060 shall be paid at the time the stipulation is filed.
(c) Upon filing of the stipulation and, if required under subdivision (b), the payment of the reclassification fee provided in Section 403.060, the clerk shall promptly reclassify the case.