Can I get additional money added to my refund if I am a college graduate student.

It's not being a student, graduate or other, that keeps you from getting the stimulus money.

It's being a dependent or even qualifying to be a dependent, under the dependent rules*.  

Under the CARES Act, if you are claimed, or qualify to be claimed, as a dependent on someone else’s return you cannot receive a stimulus check, in 2020.   If you qualified as a dependent for 2019, but will not be for 2020, you will most likely get it in 2021, when you file a 2020 tax return.

In regards to the stimulus payment, when you file your 2020 income tax return, you will be asked for information about the amount of the stimulus payment you received, and if it is less than you are entitled to, you will be given a credit on your 2020 tax return.

"In essence, the stimulus check acts as an advance of your 2020 income tax refund. This means when you prepare your 2020 income tax return, there will be a line to include the section 6428 credit (line 30 on the 2020 form 1040). The credit on your 2020 return is subtracted by any amount received as a stimulus check in 2020. If the amount you received as a stimulus check is less than the credit you are due, the difference will be included as part of your 2020 refund. If you have been overpaid by receiving the stimulus check, however, you will not be required to return any excess amount".

*There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html

There are several answers to this question.

If you pay your own tuition, from your own funds or loans in your name, you may be eligible for the American Opportunity Credit or the Lifetime Learning Credit.  The LLC can't refund more than the tax you owe from your other income, but the AOC can sometimes give you a rebate of up to $1000 even if you don't have taxable income or owe other taxes.  To get this $1000 AOC credit, you must be at least 25 years old, or if younger, your parents must have passed away.

If you are asking about the economic stimulus payment, that depends on whether you can be claimed as a dependent.  You must check the box that says "I can be claimed as a dependent" if you can be claimed, even if you don't want to be claimed, and this will disqualify you from the stimulus payment.  Deciding not to check the box when you should, just to get the stimulus credits, would be fraud.  Whether you need to check the box depends not just on being a student, but on how much you year, where you live, and who supports you if you don't support yourself.  The other answer goes into more detail about this.