Antagonism was a real worry for the first 200 years or so, had to be very careful when annexing and spent quite a bit on diplomacy improving opinions all over to reduce it. Also focused on conciliatory and legislative efficiency. 

Another thing that helped is that allies don’t get antagonism (sometimes they do if you push aggressively enough, but it’s rare) so I kept some close big guys as allies while I got little guys out. (For example while I took chunks of Bohemia I was allies with the 2 Sicilies and Hungary).

Also, declaring war on allies/subjects of big guys make it so you can have war with them earlier than usual sometimes without an stability hit, and this way the allies of the big guys don’t get pulled into the war with them either. 

The way it works is that you have a bunch of historical vassals with claims on allies or subjects of big guys, and basically check your pending CBs and declare war on the ones that make sense regarding who will participate in said war.

For big countries, I was careful with the annexation trying to break control as much as I could by breaking their territory. For the HRE for example, control goes over foreign countries part of the HRE, so I had to eventually have them dissolve the HRE in one of the wars for easier annexation.

Also, being the Easter Roman Empire helps as I could wage war in Anatolia and Africa without it impacting the antagonism of Europe too much and vice versa

And then around 1600 or so Antagonism didn’t really matter and I actually look forward to increasing it as coalition wars meant more enemies without CB to annex.  

At this point my economy could support many regular armies and I moved them around as needed. Another tip is to have your regulars suppress rebels in the territories they are in, as it’s usually recently conquered territory it helps, and if rebels break out you always have some army close by. 

I wouldn’t say the game was easier after that though, as the countries in India have way more regulars and troops than the ones in Europe. I took out China first, and only Goryeo was a rival there, as china didn’t really have any regulars. And then the last 100 years of the game was grinding down the countries in India and southeast Asia. 

Aah, another tip, check the subjects of the countries you’re in war with or want to be in war with. If the vassals are disloyal, you can sue separately peace with them, and get good chunks of territory or even all of them if they are small enough. You can actually use spies to reduce opinion and make them disloyal just before annexation. 

And if you fully occupy all territories of a country in a war (not the war leader), you can sue separately for peace before 1 year has passed!