Both are doable. MANY people do it. And you can do an address change for just one person in the house. I did it after I graduated high school.
One last comment on mail box ownership. While you may own your mail box it is under the control of the federal government once it is approved. Therefore, it really doesn't matter who owns it.
18 U.S. Code § 1705. Destruction of letter boxes or mail
Whoever willfully or maliciously injures, tears down or destroys any letter box or other receptacle intended or used for the receipt or delivery of mail on any mail route, or breaks open the same or willfully or maliciously injures, defaces or destroys any mail deposited therein, shall be fined under this title or imprisoned not more than three years, or both.
(June 25, 1948, ch. 645, 62 Stat. 779; May 24, 1949, ch. 139, § 38, 63 Stat. 95; Pub. L. 103–322, title XXXIII, § 330016(1)(H), Sept. 13, 1994, 108 Stat. 2147; Pub. L. 107–273, div. B, title III, § 3002(a)(2), Nov. 2, 2002, 116 Stat. 1805.)
noun: ownership; plural noun: ownerships
the act, state, or right of possessing something.
"the ownership of land"
The USPS has no right to take my mailbox. I am free to take my mailbox and do what I want with it including destroying it. The USPS does not have that right.
Does your state "own" your car? They have some significant legal control over how you use it?
Did the Federal government own the airplane I used? They have the right to tell me how I can and can't use it. They had the power to tell me who could work on it.