Executing the 24V upgrade.
The simple solution
For the 24V upgrade you have to remove one part (D1) on the BAM-Shield.
This is because the Arduino can not withstand voltages higher than 20V.
Then, you can apply higher voltages to the BAM-Shield without damaging your Arduino.
The only disadvantage is, that you have to power the Arduino externally.
The sophisticated solution
If you don`t like the simple way, you can mount a DC/DC converter, e.g. the TSR 1-24120 from Traco.
Use the following connections of the BAM-Shield.
and connect the TSR 1-24120 as follows
Now, your BAM-Shield is able to work with voltages from 15V up to 32V,
and your Arduino will survive.