In 20 years, I've never seen a company that was willing to negotiate over the employment contract of an employee. As a freelance consultant, I had free range to negotiate, but as an employee, the contract was always presented as "take it or leave."
I've done it a couple of times. Recently I started a new job where they had a "we own all of your IP you create at any time" clause, which is ridiculous. They agreed to change it to only include IP related to their normal business which I think is fairly reasonable.
That's probably because most people don't even think about it or bother trying. They may not even read the agreement!
I've successfully negotiated contracts several times in the past. Even once at a big company (that I knew was desperate :). As long as what you're asking for is reasonable they'll usually make the change unless it's a really big company. In that case they're not going to bother and just tell you to either sign it or go to work somewhere else. They know they have plenty of leverage and there's always someone else they can hire.
I've negotiated literally every employment contract I've ever signed. Hiring people is expensive, and by the time you've found someone you're willing to extend an offer to, there's a lot of sunk cost. That, my friend, is called "leverage".
