When 2 or more public corporations, constituting as a whole contiguous territory, are served by 1 or more intercounty drains or by a combination of 1 or more intercounty drains and 1 or more county drains, and it is necessary for the public health to supplement such existing drain or drains by constructing 1 or more relief drains, which may consist of new drains and branches and connections thereto or extensions, enlargements, branches, connections or improvements described in section 535 to existing drains, or any combination thereof, then the entire project may be constructed and financed as a whole under the provisions of this chapter and the word “drain” shall be deemed to include such a project.