Can someone tell me what hardware is needed. Part numbers would be helpful.

I had a plug with a breakout for my 2002 but the socket has changed.
Also, I think there's a box of some sort involved.

Some of the latter XC70s had a box installed at the factory as part of the normal wiring. Did you look in the left rear panel? If you have one then all you need are the 2 wiring looms.
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Keeping it running is better than buying new

The rear "electric panel" in my V70 has 16 small size fuses scattered about and 4 regular sized ones in a row. There's also a large fuse marked "40".

The panel is a surface of holes. There is no box.

What 2 looms are you referring to?
The set-up for my 2002 was a single plug and breakout which went through the body. I'd call that one loom.

Thanks for your help. I forgot to hit the Volvo dealer when I was out earlier.

The latest version I have seen have a loom from the breakout box that goes to the spare tire area, then an additional loom that goes through the body to the hitch.

If you don't have a breakout box, it gets messy with splicing wires.
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Keeping it running is better than buying new