What kind of mod? - usually, an amount is ground off the front leading edge of the standard extractor - makes like a slope or ramp so the extractor nose's edge can slide over the case rim and snap back into place to grip and extract that case. Works well. Easy to screw up by grinding just a bit too much. Also good to check that your receiver has enough room to the side - so that the extractor has room to go to the right when it goes over that rim. Is claimed by some to result in a weaker lip to the extractor - is thinner at the leading edge, for sure - if carried away, perhaps change the heat treat characteristics and make it more brittle - I don't think that you want that. When "single loading", you have lost the "controlled round feeding" for that round - so is possible to drop a shell into the chamber, partially close the bolt, pull back the bolt and get hold of second round, and forward motion will try to push second round into chamber that is full with the first round. Full "controlled round feeding" does not ever allow that to happen.
"Put one under the extractor" - that is usually done by filling the magazine full, then remove bolt from rifle - snap a round into the bolt face - then reinsert that bolt - will take some fussing to depress the rounds in the magazine, with a round on the bolt face - else the closing bolt will jam up, trying to bring a second round up from magazine. Is not meant for "topping up", I don't think - for initial loading, to get a round in the chamber and full mag. I suspect if a full mag is important, that idea to chamber one, then flip over and fill mag from bottom, through hinged floor plate, is easiest for most - is exactly the way Schultz and Larson factory instructions say to load their rifles. An S&L follower is "ambidextorous" though, so does not matter left or right first - a Mauser follower is not - have to get the left and right correct sequence to get a full mag.