First of all, consider everything that has money value in the offer and confirm whether the TOTAL TARGET COMPENSATION is really that different. You may have a higher variable or benefits in your current vs. alternative offer. Make sure you are not looking into fixed compensation only…
If this is an entry level position don't even think about it! They won't do it, they may retract the offer (I would) and even if you get what you want, in 1-2 years you'll be promoted and at that point they will give you the same salary they give to everyone else (i.e., it's only a short term gain, no long term effects there).
If this is not an entry level position, and you have relevant expertise (i.e., you are valuable not because of your potential, but you are already a real "asset), then you may have some room. However you have to understand you risk them retracting the offer. So you should only do this if it seems that they are offering you below market rates and you have to have a very tactful approach.
I am happy to discuss through private message how to approach this, if after reading all of this you still think it's a viable idea to try to renegotiate.