It depends on what you mean by conquering a conqueror. The ones who try to force it may not actually be able to do it. The best way is to somehow find common ground. We have very little to establish exactly what makes a conqueror serve under another conqueror. At what age someone awakens their CoC also matters somewhat.
Let's analyze all the ones that we have so far.
1. Kata under BM: Simply because Kata is BM's son.
2. Yamato under Kaido: Not entirely sure we can call this as being under Kaido but so far it has been through force and Yamato hates him for it and wants to kill him.
3. WB, Kaido and BM under Rocks: A bad case of conquerors under conqueror (Rocks probably was one), a lot of infighting/killing/possible betrayal. Banded together for a scheme/plan. Very little we know of it but must be something great for WB to follow Rocks. Rocks had the charisma to sell a dream which the others probably liked. Maybe they joined to get it for themselves at the end by killing others and stealing it.
4. Sengoku under WG (It is about serving under others): Was probably recruited at a young age and spent his whole career in the marines, when he awoke it, it was already too late and his career direction was pretty much decided. Plus he still became a FA so that is something like a conqueror in itself.
5. Oden under WB: WB was already against having a conqueror under him from his experience with Rocks. But Oden stayed due to his love/bond with WB and WB never called him his son like he did with the rest, but instead he called him his brother. A successful pairing. WB was the first and only option for Oden to realize his dream of seeing the world.
6. Ace under WB: Found his calling and his admiration for WB was the main thing that kept him under WB. He made a pact and honored it. I think WB was also preparing Ace to overtake him and become the PK.
7. Doffy under Kaido: Not exactly under Kaido, Doffy was his own man and king of a country, he was doing business with Kaido but he knew of Kaido's strength and was afraid of Kaido.
8. Shanks under Roger: Too young, probably didn't awaken CoC until much later, anyway he was a big admirer of Roger so would have still stayed under him maybe a little bit rebellious and independent.
9. Ray under Roger: This is one of the more intriguing ones cause this one was a successful one. Ray was called the partner of Roger (somewhat like how Oden was called the brother of WB) so there is that sense of equality and not direct subservience. The first meeting between Roger and Ray is kind of weird, Roger asks Ray to turn the world upside down. I think this is somewhat similar to Rocks selling his plan to WB, BM and Kaido (different pitch for each) but this grand plan/scheme/dream/adventure is what allowed these conquerors to make other conquerors tag alongside them. There is also Ray's epithet of the Dark King which shows his kingly ambitions, he earned that epithet, how, when and why, we don't know but he did.
10. Zoro under Luffy: This one again is a successful one and it is a mixture of the good points. Firstly Zoro agreed to be on the crew in exchange for Luffy saving his life. Zoro was helpless in that situation and this was his only option of living so he agreed. Because he agreed he is honoring that pact similar to Ace honoring his pact after losing to WB 100 times. The next is that Luffy sold his dream of being the PK, something grand/a big adventure for Zoro to really tag along. His admiration for Luffy is what has kept him on the crew apart from honoring his pact. He has been called both the partner of Luffy and his underling as well. Zoro himself has accepted Luffy as his leader but has also set some standards that Luffy must be up to, prime examples of this being Zoro's speech about bringing Usopp back and his comment in Fishman Island after Luffy using his CoC.
So to conquer a conqueror successfully the leader must be able to sell a grand scheme/plan/dream/adventure. The dream should in some way be meaningful to both even if for different reasons. Trying to use force to conquer a conqueror has so far not successfully worked (Kata is a wimp). And most importantly the two should have a deep understanding of each other and a great bond of friendship.
