The following solution is not the most maintainable one (it uses prefixed java classes, even if it is quite stable packages)but works and is 100% Studio

Here is how I did it:

• Fetch > something

I get the document that stores the list

• Execution Context > Set Context Variable

parameters:

name: listOfSringTmp
Value: @{new java.util.ArrayList()}

Temporary variable where the list of all elements will be stored.

• Scripting > Run Script

parameters:

script: java.util.Collections.addAll(Context["listOfSringTmp"], Document.getProperty("mySchema:myField"))

We add values stored into your document

• Scripting > Run Script

parameters:

script: Context["listOfSringTmp"].add("MyNewValue")

And we add the new value

• Scripting > Run Script

parameters:

script: Document.doc.setPropertyValue("mySchema:myField", Context["listOfSringTmp"].toArray())

And we set back the list into the document

• Document > Save

I save my modification.