I would suggest thinking about this as stacks of thirds rather than as changes to another triad. As I’m sure you recall:
Major Chord: Built as a Major 3rd between the root and the middle note and then a Minor 3rd between the middle and top note
Minor Chord: Built as a Minor 3rd between the root and the middle note and then a Major 3rd between the middle and top note
Diminished Chord: Two Minor 3rds
Augmented Chord: Two Major 3ds
This is how you would describe the four basic triads theoretically and it has the benefit of not needing to be referenced to another chord.
Example: Exam says “Build a diminished triad on the following note” and there’s a D written. You’d just write a minor third (An F) and then another minor third (An Ab) and you are done. It helps you know what enharmonic notation to use. Here, F to Ab is a minor third…and F to a G# is an augmented second and would NOT be correct .
I’m not suggesting the previous answer is wrong, simply incomplete.