With the CAGED system for minor chords you can play any minor chord in five different positions on the guitar fretboard. If you haven't already, please have a look at the introduction of the CAGED system.
The CAGED system for minor chords uses the open minor chord shapes Am, Em and Dm introduced in the basic minor chords section, plus two new chord shapes for Cm and Gm.
Here are the three basic minor chord shapes Am, Em and Dm plus the two new chord shapes Cm and Gm combined on the fretboard:
Below is a list of chord diagrams that result when applying the five minor chord shapes to the root notes C, D, E, F, G, A and B. Here is help on how to read chord diagrams.
Keep in mind that it's often possible to change the chord shapes slightly, e.g. by omitting duplicate notes or by adding an open string to the chord shape (for example, when using the D minor shape to play an E minor chord it's possible to add the low E string - this is indicated by the grayed out letter at the bottom of the chord diagram).
Also not shown below is that some barre chords can be played with the thumb over the neck instead of barring the strings with the index finger.