After any district is established the area embraced therein may be altered in any of the following ways:

(1) The Secretary may add to such districts any public lands which, in his opinion, should be made a part of the district.

(2) The Secretary, subject to existing rights of any lessee, may exclude from such district any lands which he determines are no longer valuable for grazing purposes or are more valuable for other purposes.

(3) The Secretary may enter into cooperative agreement with any person, in respect of the administration, as a part of a district, of lands owned by such person which are contiguous or adjacent to such district or any part thereof.