Double grouping.
I'd be inclined to pay attention to your bag set up and watch the flags if you are getting double grouping. I haven't been at this BR thing for long but it has been my experience that these rifles are very easy to tune for since they are so much more predictable and repeatable than say a factory varmint rifle. I assume you are talking about a bench rest rifle ?
It seems to me that so long as the rest set up is good and the rifle is sound the loads that are miles away from a good load will just be big round groups, say scattery 0.5's. The same would apply to components that the rifle just doesn't like, say a certain bullet. Once you start to get close to a decent load the groups will tighten up and show mainly vertical spread to maybe 0.3 or so. Once you start to get the load going well the vertical will reduce and the rifle will shoot small round groups or hopefully "dots" !!
If you are getting horizontal double groups you are probably missing something in the wind reading or doing something on the rifle, pulling sideways on the trigger or not having the bags aligned with the target so the rifle is rested in a stress free state or any number of other possibilities.
If you are getting double grouping vertically you might want to look at the shoulder position for consistent pressure or consistent gap if free recoil, also trigger hand on grip etc etc. If that all seems OK it may just be the load isn't right and the number of shots simply gives you a gap between 3 and 2 or 4 and 1 or whatever. If you had a double group to say 0.4 with 5 shots it may become a string of shots spread vertcally to maybe 0.5 if you fired 10 shots which would look more like a bad load than some other issue. See what I mean, the double group would become a string and no longer a double group at all.
It seems to me that once the load overall is getting close in terms of powder weight and seating depth changes in either will really only alter the vertical spread of the group. I wouldn't count on just changing seating depth to cut out possible double group scenario.
Get the powder weight close with the bullets on the lands, tune the seating depth to get the best depth and then fine tune the powder. Bingo !! Then you just need to keep the tune in different conditions !!
The only proper double grouping I have ever experienced was with a varmint rifle with a bedding issue.
Just my thoughts, like I said, I am no expert.
Bryce