Whenever any local improvement shall be of such nature and character that the special benefits resulting therefrom extend beyond the boundaries of the property abutting the improvement or whenever the special benefits do not accrue to some or all properties abutting the improvements, but to other properties, the council may create a modified local improvement district, which shall include as near as may be determined all the property especially benefited by such improvements. Provided however, that by unanimous agreement of the property owners to be assessed, properties may be included or excluded from the local improvement district regardless of whether they are specially benefited by the improvements. When such district is created, all property therein shall be assessed for a portion of the cost and expenses of such improvements, to be determined and fixed by the council when the district is created.