back for

back (someone) for (something)

To support someone in some pursuit, often election to an office. I'm backing Caroline for student council president—here, have a button!
See also: back

back someone for something

to support or endorse someone for something, such as a public office. We all back Tom for president. I am backing Jane for treasurer.
See also: back
References in classic literature ?
I think that is good advice to follow," put in Tom, "for we do need our goods; and if we reached the settlement ourselves, we would have to send back for our things, with the uncertainty of getting them all.
She answered seriously: "I thought maybe you couldn't come back for me.
She opened the door of the drawing-room, and stood back for him to pass in, entering herself behind him.
When acute back pain occurs, the AAOS recommends lying on your back for 20 to 30 minutes and applying ice packs to reduce initial pain and swelling.