Dealer pays "invoice". You're plan code is typically a small amount above that, say $500. So very little room if any to negotiate, and no they don't get reimbursed for plan buyers if I remember correctly (this was 8 yrs ago, things may have changed) because technically, it's over invoice cost. Rebates, which are paid by the manufacturer can make it lower. The dealer is then reimbursed for the rebates. So they don't fiddle with adjusting those. Plan buyers with cash, make them JACK SQUAT.
Normally, if you use a plan code, they won't negotiate. However, where you have room to negotiate is if you are trading in on something. And that's also where they try to make their money. If they know you're a Plan Buyer, they won't waste time haggling, you have your set price. But if they can get $20k for your trade in, and only give you $17, they can make $2000 profit right there ($1,000 for inspection, repairs, etc). So they will hammer you on your trade-in value, versus hammering you on the new car price.
If you have no trade-in, you're pretty much set price except for financing. They can make their money back there as well, and trust me, they're very good at it. You'll typically get better rates from a Credit Union, unless you're going for 0% financing. And don't forget all the BS fees they add. Some are legit, some are not, it's up to you to know your state's actual requirements. They always say "it's required by law". Not all of them, but there are so many, most people can't keep up with which is which.
If I was a plan buyer, I'd shop my local credit union and their financing rates. Then go talk to the dealer, and their financing and compare. That's where you're going to have room to negotiate.
The only way to get lower, is to forget being a plan buyer, go for an older vehicle and offer invoice minus rebates. Wet their appetite with you walking into their financing office. Get a number you want, and then either have your check ready, or go with their financing.
