The best company to negotiate with is the one you already do business with, in my experience. It's called "customer retention." They spend millions getting you to sign up, they will spend a few bucks to keep you.
I happen to also be a customer of T-Mobile, and I routinely get free extra data, I've gotten a free signal booster (boyfriend's company would not budge on $200 for that), $50 bonus for trading in an obsolete phone, all because they see I've been loyal since 2003. Over those years, they've been stricter or looser as times change, but a reminder that "all these other companies are throwing cheap offers at me." And ask for customer retention.
I used to do the same thing with ATT until I cut the cord.
Medical bills, luckily I haven't had to deal with, but I've heard you can ask for an audit of a hospital bill and they will take off many of their bogus or inflated charges. Wait, come to think of it, I have sort of negotiated with chiropractors and massage therapists, but more at their prompting when I was about to quit.