First of all, I'd say, wait for the actual offer to be made - you might be surprised to see the amount.
That said, it's good to have a backup plan in place. Getting to the question
how likely a company accept a counter-offer for a graduate role?
Onlyonly the company (relevant authorities) can tell. But you'll never find out if you don't ask.
One thing I say always: Never accept an offer knowing that you'd not be happy with the benefits.
- You don't absolutely need it (i.e., Financial problem)
- You'd not be happy with the benefits. (i.e., the long run outcome)
It's not only the paycheck, consider all the perks and benefits that you'd get with the job, compare it against other offers (if you have) or against your expected bucket of benefits, and make the call.
When you ask for the negotiation, it can be seen as self-awareness and having the knowledge about the industry you're in. You need to present your arguments tactfully - never mention being "better than peers" - that's not your job / scope. You mention
- How your skills are relevant for the company / business and how they will have a positive effect on the company
- What all positive feedback you've got
- How you feel your pay scale should be adjusted to match with the industry / market standard.
Let them reflect back on that. At most, your proposal will be rejected. Be prepared to handle that situation - whether you want to work with the previous pay structure which would be offered initially and or look for opportunities elsewhere.