Anyone familiar with the Rolling Stones’ lyrics to “Let It Bleed,” will see connection to the eroticism in a title like “All Over You.” But to push that sexually aggressive voice more, Dylan adds a stalking predator voice to the lyrics, not present in “Let It Bleed,” as in the last four lines of the next to last and last verses:

Well, if I’m ever standin’ steady
A-doin’ what I want to do
Well, I tell you little lover that you better run for cover
’Cause babe, I’ll do it all over you

Well, after I do some of these things
I’m gonna do what I have to do
And I tell you on the side, that you better run and hide
’Cause babe, I’ll do it all over you

At the end of a performance of the song on July 25, 1963, Dylan says, “That’s kind of a mad song.”  Mad?  Angry mad? Mad as in a madness? Either way, the humor in the song is underscored during the whole performance and from the audience’s response during and after.

For me, the crucial word for a less on the surface interpretation is found in the word “over.”  The singer in this song is not mad at the target of his obsession but at himself for not doing all he could do over her, as in because of her, as in being head over heels in love with someone, or not being able to get over someone. If I had another chance to do it all over, and watch out, I will, is threatened all over the song, I would do it all because of  you (her).  The singer is promising that he will do it right if he gets a next time, and that next time will involve him being totally focused on her; everything he does will be for her.

The rhymes are alternating; in each of the 12 line verses, lines 2 and 4, 6 and 8, and 10 and 12 rhyme.  There’s internal rhyming starting with verse 2 found in lines 1 and 3, and that pattern continues in verses 3 and 4.  The internal rhymes are clever and arguably the most amusing, as in,

I’d jump up in the wind, do a somersault and spin.

And I grab me a pint, you know that I’m a giant

The terminal rhymes consist of do/you at the end of three of the four verses.  That’s  a rhyme often repeated in “All I Really Want To Do” as well.  I see the the meaning of this song similarly.  In “All I Really Want To Do,” all he really wants to do is not mistreat her; though in “All Over You,” he might seem to threaten mistreatment, it all depends on how “over” is interpreted.  To appreciate the double-meaning in this song, as in, say a song like “Rainy Day Women #12 & 35,” we may need to get over what doing something all over someone might mean.

Here’s that 7/12/63 performance: