Remember the reason for shooting groups is to provide a "sample" of the rifle's accuracy. The sample is then use to predict where the next bullet will strike. The higher the sample rate (more shots fired) the more predictable your next shot will be. statistically, a 10 round group gives you a 90% prediction, a 5 shot group gives 45% prediction, and a 3 shot group gives a 27% prediction.
Rifle barrels heat up quickly and that heat change will cause the groups to spread. You will get false samples if you allow the barrel to get too hot. I like to shoot 3 shots, spaced a couple minutes apart, then let the gun cool down for 15 minutes and repeat 3 more shots. I fire a total of 9 rounds per load. I measure each group then average the three. From that data, I can predict with 81% confidence, the next shot will be within the average group size. I shoot each group at a different target and try to "call flyers". That way I can eliminate most of the human error and just deal with the rifle's accuracy.
No matter how many shots you fire, the key is to let the barrel cool down between rounds. The chamber heat will transfer to your cartridge and heat up the powder. All powder burns faster the hotter it gets. This will corrupt your groups because the muzzle velocity will change. I wait to chamber a round until just before I'm ready to shoot.