Anyway, the way I negotiated was very simple. Basically a version of ”I understand that this is a good salary relative to my local market, but I am not even looking for jobs in my local market. I am comparing your offer to offers from other US-based companies that I received for remote work.”
That was it. The part of other offers was true of course (even if for companies that I wasn’t too excited to work for). No need to even reply to their arguments of “company policy”, “cost of living”, whatever. I only have to state my point of view.
There is also the topic of me not receiving benefits like health care and 401k and other stuff that American employees get. I didn’t use this argument (didn’t occur to me), but I have the impression that this was considered in their calculation in how much to raise their offer.