You can. Disconnect it from one person's iCloud, connect it to the other. We did it with our cat's AirTag when I got a newer iPhone, so we could use the more accurate location.

I do wish there was a share feature, though.

The lack of integration with family sharing has made AirTags mostly useless for me.

It’s a genuinely baffling omission.

Especially given the existence of Find My, which makes it easy to set up phone tracking so we can "stalk" each other. Apparently it's okay to track wife's phone but it's not okay to track my wife's backpack.