Concubines don't really change anything as far as I've seen. You'd think it'd give you more kids but I think how it works is that you have some sort of "child counter" on your character and every time it activates, it just assigns an eligible lady to have your kid. Your best bet is nailing as many of the affair type events as possible and hoping for bastard sons.
Though, children are an exponential thing. Your ideal start would be to just have as many of your children have lustful traits and hope for the best. Don't know about thousand, but hundreds of living members is certainly feasible.
You can help this along by landing as many of your dynasty members as possible. This will help them get wives. You don't have to give them counties, even baronies are fine, which are probably better as they can't rebel against you that way. Not to mention the AI doesn't really care about barons either, so they wont have their lands confiscated. You get baby breeding machines.
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I've almost finally finished my ironman Swabia game. Year 1320 now, so about 100 years more. I got about 200,000 points total right now, which is good. My power is so incredible that I literally obliterated the entire Sunset Invasion with their 140 000 men without them taking a single province. I smashed them so hard that when they landed a second invasion force to attack the collapsing Muslims, I just casually walked down there with my existing levies and crushed that too. I crushed both Mongol hordes several times, something I've never managed to do before, and I did that with just my retinue armies alone.
My capital city has every single thing constructed. In fact, I have 100% completed my research trees for commerce and social stuff so some of my advisors actually have nothing to do.
I earn more than 400 gold per month, and double that in prestige. Every single one of my children basically get born with the +20 prestige modifier because they get so much of it. I can't actually use up all my gold. I can have every single mercenary army hired permanently and still draw big profit. This is made even cheaper by the fact that my dynasty both vassalizes and directly controls every single holy order as well as the Papacy. I can get the pope to excommunicate anyone I wish because he has to follow my whims.
I have 70,000 men available permanently as retinues. It's a bit obscene and I split them up into several armies just wandering around my massive empire arresting people. I never, ever see any more vassal rebellions because of this too, as they judge their power by your current available power. So even if 50 of my vassals banded together, they couldn't field the 100,000+ men total I have available at my disposal. And let's say the holy orders were plotting against me and I got the vassal rebellion warning, I could hire some mercenaries or raise some vassal levies to boost the number and they'd give up.
The amount of positive relations all my characters garner just by existing is so massive that getting a -80 relations modifier from banishing people is irrelevant to me. And even on the rare chance I get enough to make people dislike me, my imperial military strength is so high no one dares to rebel. I haven't had a succession crisis in centuries.
Peace through absolute power.