Setting aside GDPR - Setting a 3rd Party cookie already fails in enough situations (Safari) that if you really wanted to trace a user cross several site, you'd require a different solution anyway.
What kind of other solution do you think about ?
You could do something like an iFrame, with the parent site passing information to the frame. Here's an example: https://medium.com/building-contently/tracking-people-across...
Same question: this iFrame would be used to store information related to the user across websites, it kind of works like a cross-domain-cookie-replacement : could GDPR make these kind of tooling illegal ? Should we display a very specific popup to tell the user what those scripts really do ? And have an opt-out option ?