The legislative body may establish, change or modify the grade of and order to be done in, over or under the whole, or any portion, either in length or width, of any one or more of the public streets, places, sidewalks, highways, roads, or property or rights of way (including tidelands and submerged lands owned by any city) within the limits of the city which is carrying through the proceeding in question, and also into the limits of other cities or extending from the city through or over one or more other cities, or extending through or over one or more cities and into a county or extending along the exterior boundary between a city and a county, or along the boundary between two cities, whether wholly or partly within or without the boundary, either singly or in any combination thereof, any of the work mentioned in this division under the proceedings described in this division.