Everybody Wants Some

So you want a much bigger raise than what they are offering at that shiny new employer who just made you an offer?  Can you counter with what you really want?

Before you talk numbers, it is useful to understand how the "other side" (employers) think about salaries.

Companies of any appreciable size (and by your salary I assume we are talking about a US company) have a standard way to determine pay: Market price.

Market price consists of two things:

1. Mostly, market price is a summary of what other companies are paying similar people with similar skills and similar experience to do similar work in the same geographic location. This is not based on a few examples that might be outliers or anecdotes. This is based on vast surveys of many employers and hundreds of positions. Before you ask for a 40% raise, do some research online about salaries of similar positions in your area. You may find that the averages are similar to what you make now. Or not. But asking for significantly more than the market rate is seldom successful, even if your current salary is far higher. (Such a situation is usually interpreted as the candidate being over qualified for what the role requires.)
2. Secondarily, market price can be very specific. If you have competing offers that demonstrate a higher number than a particular employer is offering you, that can be used as a basis for asking for a higher offer. But be sure to do the math and understand that base salary is just one component of one's compensation. Bonus, stock, benefits, etc are all factors you should consider. (Note that I assume you do NOT have a higher current salary, otherwise it would be unusual to receive a lower offer than what you currently make.)

And, finally, at the end of it all, how do you want to be spending your time? Doing what? With whom? For whom? Sometimes, salary cannot compensate for problems in these other areas.