Multiple mouse cursor objects - is this possible?

yes, you can even use different "cursors" (more appropriately, moveiclips behaving as cursors) in the same frame if you wanted.

but for different cursors on different frames:

frame "cursor1":

stop();

// you may need to remove the other "cursors" depending on your possible navigations
stage.addChild(greendot1);
greendot1.mouseEnabled = false;
greendot1.addEventListener(Event.ENTER_FRAME, gd1F);
function gd1F(event:Event)
{
            greendot1.x = stage.mouseX;
            greendot1.y = stage.mouseY;
}

Mouse.hide();

frame "cursor2":

stop();

if(greendot1.stage){

stage.removeChild(greendot1);

}

// you may need to remove the other "cursors" depending on your possible navigations
stage.addChild(greendot2);
greendot2.mouseEnabled = false;
greendot2.addEventListener(Event.ENTER_FRAME, gd2F);
function gd2F(event:Event)
{
            greendot2.x = stage.mouseX;
            greendot2.y = stage.mouseY;
}

Mouse.hide();

frame "cursor3":

stop();

if(greendot2.stage){

stage.removeChild(greendot2);

}

// you may need to remove the other "cursors" depending on your possible navigations
stage.addChild(greendot3);
greendot3.mouseEnabled = false;
greendot3.addEventListener(Event.ENTER_FRAME, gd3F);
function gd3F(event:Event)
{
            greendot3.x = stage.mouseX;
            greendot3.y = stage.mouseY;
}

Mouse.hide();