My local Mercedes dealer took the first £3k of a car purchase on AMEX but said that was the max they would take. The rest had to go on a debit card.
In another branch they had done about £3k of repairs but would not take Amex at all, saying although their systems could process it, the commission was too much. I said I'd pay the difference in charges if it was reasonable, no one actually knew what the difference was. After a bit of pushing the Finance people checked, found it was only £12, took the AMEX and waived the £12.