You need to understand that with most organizations, they have salary guidelines that HR and hiring managers works with. It's not like they can take you from making $80,000 per year and give you $160,000. No matter how good you are, it just doesn't work that way.
With big companies, the basic strategy is always that you should get two offers. Not one but two. You have to time this out around the same time so that in this way, there's a certain amount of pressure on the employer. After all, from their standpoint, they have spent a lot of money interviewing and assessing candidates and deciding that you are the right one.
What you want to be doing is getting two firms in play. They're not going to bid aggressively against one another. It's not like they're going to say, "We're going to offer you $120,000."
"We are going to offer you one $130,000."
"When you change your mind and we're going to offer you $140,000!"
They will work to exceed something; don't talk with you about some of the benefits that they offer you. They may "goose" certain things but when push comes to shove in the big company market, normally, the lowball bidder tries to match the highball bidder. They can go back to the highball firm and say, "I have 2 offers at the same level. I prefer yours. Can you do a touch better?"
Watch my video called, "The Easiest Way to Negotiate A Higher Salary for Yourself." What that technique will do is get them to boost the offer little bit more so that you up the ante.
Now, at small companies, you get two offers, a big company and a small company, often the small company will do a little bit better, but they will never really match the big company. The big company just has deeper pockets. Maybe you'll get more benefits, more stock options, more things along those lines that will turn you on.
Recognize that a small company or a start up, sometimes their reaction is to go, "You know, if you are considering that another firm, you are not our kind of person." You have to be cautious with small firms when you are doing small company versus big company competing situations.
Two small companies. 2 startups. They get into (excuse my language) pissing wars with one another where they are beating down the other firms ideas, where they are talking with you about how good they are. You really need to bring them back to the money.
"I really appreciate more options here."
"Well, this is what we give out to people."
"I know. AND I would like more options here. I would like to get more money."
Do something that pushes them. Whoever comes in a little bit higher, that's the one you go to.