Different beekeepers are trying to achieve different objectives, and while some principles remain the same, the routes are different.
For example, some here will be trying to turn around a treatment-dependent apiary, while others like myself are starting from scratch with bees we calculate may be capable of being treatment free from the start. (My best bet are ferals, as in the UK no bred resistant bees are available)
For the first group, a driving strategic aim will be to try to locate the most resistant, and requeen the worst, thus maintaining numbers.
For the second group the strategy will include building numbers first - to be able to lose bees without having to start over, to be able to start to raise the resistant drone population, and to have bees to make bees. This thread is addressed to the mostly to the needs of this second group.
We'll want to quickly form a view of best goers, and have them raise lots of drones. One of the dangers it appears to me is that in our rush to build numbers we make splits, and that doing so both obscures the resistant qualities of the mother hives and perhaps inhibits drone raising in them too. Both these things could lead to unnecessary failure in the breeding process.
If -if - mother hives are protected from mites through the act of splitting, we might mistake less or unresistant hives for resistant ones - and graft and split more from them. Or build them, and have them put drones in the air, only to find them overloaded with mites in the autumn.
If - if - mother hives _are_ resistant, then splitting might reduce drone numbers - and they are as important as good mothers.
Both these things could lead to rapid loss of apiary resistance.
That's why, while I appreciate the need to build numbers fast, I'm cautious about splitting as a way of getting there. It could easily lead to failure by inducing false readings as to real mite resistance qualities and resistant drone numbers.
And that's why I'm going with dedicated brood/bee raising hives, and dedicated drone hives.
Preserving true readings (of mite-management capacity), and acting upon them, is everything. Anything that interferes with that essential assay process threatens to undermine the whole effort to raise bees that can cope with mites themselves.
I think routine splitting for increase (whether building numbers or sales) is a dangerous road to go down. There is a more professional way. Manley speaks of queenright cell building colonies (of a kind he specifies) as rearing 'lots of choice drones'. An integrated methods that needs all the needs of queen raising, drone raising, brood raising and providing true readings is possible. Maybe others in the same position would like to talk more about this here?
 Honey Farming, p106 - available as an ebook