No.

You can create another factions ideology similar to your own. But the game itself will never see that ideology as part of its own.
Just like in real life.

Judaism, Christianity and Islam are all Abrahamic religions. But if you look at each description of God they are clearly not the same God. And if you look at what they believe in, they are not the beliefs.
While they have many things in common with each other. They will absolutly murder each other because their beliefs fundamentality make the others and enemy.

You can't create a situation where you have "multiculturalism" when they all believe they are the same. If you want individuality and diversity, you can not have uniformity. B isn't A, and A isn't B. C will always see itself as something that isn't A and B, and the same goes for A and B.

I thiink I might have found a mod that might make it possible, though I still have to try it out.

https://steamcommunity.com/sharedfiles/filedetails/?id=3768592866

This mod just popped up on the workshop:
https://steamcommunity.com/sharedfiles/filedetails/?id=3817919332

One ideologion with different castes/social classes.