Maybe it's lame and old fashioned... but I've had success with explaining things with flow charts. Make some boxes to represent APIs, make some cylinders to represent DBs, etc, draw some lines to show how things connect. Pick some pretty colours, managers like that. Think more on the lines of explaining to a child how things work.

Once you have that picture you can point to things on it and say "we can add some code here, and a few tables here to provide the feature." You can add more boxes and lines on another version to represent the new software they want to add to the flow, and they will be able to visualize how that makes things more complicated. Then talk in terms of time to maintain this new software that makes the process more complex... "My estimate is it will take 200 hours to implement this and an additional 100 hours per year to maintain it." Yeah, it's mostly going to be numbers you pulled out of your ass, but if your boss is the kind of person that pulls ideas from their ass, they really can't dispute what you're saying. And they will hopefully be capable of converting the time estimate into a money estimate themself and they will come to the conclusion on their own that your preferred approach is better on their own.

The trick is to make them think it was their idea.