it really depends on the vendor,most on line vendors work on such a low mark up that it's very difficult for them to discount anymore ,But Many would make the effort to compete or give you the same price as the one you have seen somewhwere else.
Here's an easy example: did you ever use the diamond serch engine here on PS? Some diamond prices are marked "p" meaning that sellers would match the lowest price posted for the same stone. The difference is usually below 10% of the marked price... but I did not make many enough such comaprisons to draw stats.
From the same serach, you can easily check the size of price variations for stones with simmilar proportions and same color, clarity and weight. Cut quality and seller's premium account for these variations (which can be quite large). The whole interval is usually much larger than you can negotiate anywhere and you will have to factor in cut quality, to boot... but such info makes for a start, I guess.
You will probably conclude that the prices of H&A are more consistent and cut quality much easier to recognize and "factor in", just because it is much better described than a GIA cert does. Overall, these stone sare more valuable due to their specialty cutting, so you may want to take them off the list, when browsing non-ideal cut prices...
Depends on the store/person your dealing with to get the stone and how well connected they are for getting stones. One would be amazed at the prices you can get if you cut out some of the fluff. Even online, some of the smaller companies and design firms can offer really good prices if you do some searching, the less the overhead, the lower the price and more room you have to work with.