What should be followed when choosing additional colors that are not included in the color palette?

Question

User interface

I use a two color approach (accent and fill) in my design.
I ran into a problem that in some elements I need more colors, for example, for success, alert caution warnings or for styling elements of type meter, which just also has these three colors of similar semantic content (success, caution, alert).
The challenge is to find the optimal value for these colors. I'm looking towards pure colors, but perhaps there is already a certain standard that everyone follows)
What system can be followed?
As an option, I'm also considering the ability to dynamically create these colors based on the existing palette, so that everything is feng shui)

Answer 1

>> Than to be guided by
Taste. Services like can help:
https://color.adobe.com
You fill in your base color there and see what palettes the service will generate. Very comfortably.