Haven't heard of any Thule or Yakima roof box that isn't compatible with the other manufacturers bars (round, square, aero).

This seems obvious, but if you have a hatchback, make sure that you can open it with the box on top.

Are you close to an REI? Both Thule and Yakima are 20% off through May 29, so you might not save much money buying used vs. new and the newer boxes have a bit more structural rigidity and open on both sides (vs really old ones)

Also consider what you are going to put "up there" and the maximum weight your cross bars can handle. Most factory racks have a lower limit than a complete yakima/thule system.

I have a Thule and use it on the factory racks on my Rav4. I have friends who have one and can not use it on their Santa Fe for some reason.

So yes it can work with other bars but not all of them.

The way the Thule clamps are it should be able to clamp over any roof bars. PM me if you're interested in a Thule Atlantis, used on one trip.

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I miss YaHey

Inno, Malone, and Sportracks make them too. Sportracks was a Canadian company, the Thule bought them and made them their economy brand.

Basically all of them fit all bars - square, round, aero, and factory. Some of the cheap, old ones don't fit aero. Most made in the last 10 years, you can download the instructions online and check out how they attach.

Worst case fab some DIY clamps. This isn't rocket science.