You can negotiate your own deal certainly. If the house is listed with a Agency, you will still pay the commission, all of the commission will go to the listing agent. If you are buying a FSBO, there will be no commission.
The commission is decided when the home is listed. The listing agent negotiates with the seller for the commission. If those papers are signed, the seller has no choice but to pay, so there is no negotiating commission into your sales price or offer. It will be paid. If this is the case, you are better of being represented as well.
If you are working with a FSBO, they should have some negotiating room.