Mo. Rev. Stat. § 64.875
The regulations imposed and the districts created under authority of sections 64.845 to 64.880 may be amended from time to time by the county commission by order after the order establishing the same has gone into effect but no amendments shall be made by the county commission except after recommendation of the county planning commission, or if there be no county planning commission, of the county zoning commission, after hearings thereon by the commission. Public notice of the hearings shall be given in the same manner as provided for the hearing in section 64.815. In case of written protest against any proposed change or amendment, signed and acknowledged by the owners of thirty percent of the frontage within one thousand feet to the right or left of the frontage proposed to be changed, or by the owners of thirty percent of the frontage directly opposite, or directly in the rear of the frontage proposed to be altered, or in cases where the land affected lies within one and one-half miles of the corporate limits of a municipality having in effect ordinances zoning property within the corporate limits of a municipality, made by resolution of the city council or board of trustees thereof, and filed with the county clerk, the amendment may not be passed except by the favorable vote of two-thirds of all the members of the county commission.
§ 64.875, RSMo