Green’s Dictionary of Slang

shack up (with) v.

[shack v.; note all senses can be used both transitively (usu. constr. with with) and intransitively]
[1930s+] (orig. US)

1. to live with a sexual partner.

2. to have sex with someone.

3. to pick up, for sexual purposes.

4. to live or reside, usu. temporarily.