my_solution

/* Create a new class called AParams */
public class AParams{
    AParams();
    get/setArgument(String argument);
    get/setOtherArgument(String argument);
}
public class AFactory {
    public A create(String name){/*Create the correct A*/}
}

public abstract class A {
    public abstract void doStuff(AParams argument);
}

public class A1 extends A{
    public void doStuff(AParams argument){/*some usage of argument*/}
}
.
.
.
public class AN extends A{
    public void doStuff(AParams argument){/*some usage of argument*/}
}

public class B extends A{
    public void doStuff(AParams argument){
        /*I need otherArgument too!
         * And it's not in the UserInput class which I
         * cannot change/inherit/modify in any way :|
        */
    }
}

public class Interpreter{
    Interpreter(){}
    public Stuff interpret(UserInput userInput)
    /* read the user input and do MANY things with the input
     * one of them  might be calling AFactory.create
     * and in the end Runner will get its A instances
    */
}

public class Runner{
    public static void run(){
        /* Runner needs otherArgument which B needs but
         * for something else
         */
        for(String argument : listOfArguments){
            for(A actualA : listOfA)
                AParams params = new AParams();
                params.setArgument(argument);
                params.setOtherArgument(otherArgument);
                actualA.doStuff(params);
        }
    }
}

public class EntryPoint{
    /* Has both UserInput and otherArgument
     * it calls the interpreter.
    */
}