If they won't negotiate on price, consider negotiating for upgrades. Ask for an extra year on a license, or to be certified for commercial trucking.
...I joke, but in Thailand, where driving schools can administer the driving tests, not just the DMV, people do shop around for driving schools for various reasons.
Even then: Things can be negotiable. Haggling can be rejected, but that's not a hard-and-fast rule.
(It's anecdotal, but: During my brief time in big-name department store retail, one of my duties was operating a cash register. All cashiers there were able to discount anything by up to, IIRC, 30% -- without getting any special approval. It just took a few button presses.)
I think we were allowed to discount products up to 10% when I was a computer technician in a big retail store. I always felt it would be frowned upon, it wasn't something we did often.
Services, though, were very flexible. Nobody was looking at the receipt, just the work order. 80% of something beats 100% of nothing every time.