Ala. Code § 22-21-340

Neither the formation or dissolution of one authority hereunder nor the reincorporation hereunder of a public hospital corporation shall prevent the subsequent incorporation hereunder of another authority or the subsequent reincorporation hereunder of another public hospital corporation pursuant to authority granted by one or more of the same authorizing subdivisions. Further, any county may authorize the incorporation of an authority hereunder notwithstanding the existence in such county of a public hospital corporation designated as the agency of such county with respect to public hospital facilities therein pursuant to the provisions of Division 2 of Article 4 of this chapter.