By Jessica Dickler

When it comes to going to college, there is only one notification more significant than being admitted: the financial aid package. But unlike getting in, it's rarely black and white.

"The reality is that a lot of colleges will negotiate, they just don't advertise this," said Eric Greenberg, president of Greenberg Educational Group, a New York-based consulting firm.

Financially, there is a lot at stake. With college costs steadily increasing, tuition is a major concern when selecting a school for this year's high school seniors.

At public four-year institutions, costs for the 2015–16 school year rose to $19,548 from $16,178 five years ago, according to the College Board. Tuition plus room and board at four-year private universities was much higher: $43,921 on average.

To ease the pain of that hefty tab, appealing for more aid "could add up to tens of thousands of dollars over four years," said Kalman Chany, a financial aid consultant and author of the Princeton Review's "Paying for College Without Going Broke." Here's how to increase that initial offer.

The first thing families should do is look at what kind of aid they received and from what kind of school. "What may look like the largest offer might not be the best," said Rick Castellano, a spokesman for Sallie Mae, which provides loans to students.

Families need to understand the difference between scholarships and loans. In other words, "what needs to be paid back and what is free money," he said. "It's about maximizing money that you do not have to pay back."

Also, when it comes to appealing for more aid, private schools typically have more money to spend to attract high-caliber students. "They know that if they don't come in with enough money, other schools will outbid them," Greenberg said. Those schools will have the incentive, and the means, to increase their initial offer.

Are there other financial factors that increase the need for aid? If there are issues beyond what was noted in the financial aid paperwork, like an older sibling who moved back home after college, care for elderly grandparents, increased health-related expenses or the loss of a job, those should be explained to the school and documented, if possible.

Alternatively, if the financial aid packages from other, comparable schools were better, that is also worth bringing to the school's attention. "That could incentivize the school to be more flexible," Greenberg said. Even a better school offering a lesser reward is worth noting — more so than a more generous offer from a lower-ranked school, he said.

"Be subtle," Chany said. "Many schools don't acknowledge that they meet other school's offers, even though they do."

The next step is to call up the financial aid office and ask if they would prefer to set up a face-to-face meeting or correspond by mail. "It's typically better to do it in person but follow the protocol the college sets up," Greenberg said.

Whether in person or by mail, lay out the reasons for your appeal as well as any documentation you have, including copies of the other relevant financial aid offers, Chany said. Appeals mostly happen by committee, so any new information should be presented clearly, he said.

"Be succinct," Chany said.

"Reach out to a few schools that feel like very good fits," Greenberg said. If you are already getting quite a bit of money, appealing the package can be a waste of time. But more often, it isn't.

"In some cases, a school has matched other awards or given even more money," Greenberg said of his experience with appeals. Although not that many people know about the appeals process, "it's not a 'secret,'" he said.