Yes, some fatty acids make soap more alkaline than others. There's a good discussion of this in Kevin Dunn's book Scientific Soapmaking. He may also have it on his Caveman Chemistry website, but I haven't looked to confirm that. I also cover this topic in my articles about soap pH and alkalinity:
https://classicbells.com/soap/pH.asp and
https://classicbells.com/soap/alkalinity.asp
"... I am guessing there is a limit when CA is added when it comes to solubility..."
I consult Wikipedia rather than guess; it's a quick and legit resource to get basic chemical properties.
In water at room temp (20C/68F), Wikipedia tells me you can dissolve about 62 grams of citric acid in 100 grams of water. Yes, that's a limit, but that's a really high limit -- citric acid would be a "highly soluble" chemical in water to most chemistry folks.
https://en.wikipedia.org/wiki/Citric_acid
The amounts of citric acid normally used as a chelator in soap are far, far lower than this.
I strongly second this!