Yes this is possible. I'm using this mechanism in my own application.
What I do first is make an FXML with the menu bar and an AnchorPane who contains the content. This FXML is loaded when the application starts.
I use a Context class (based on the answer of Sergey in this question: Multiple FXML with Controllers, share object) which contains a method ShowContentPane(String url) method:
public void showContentPane(String sURL){
    try {
        getContentPane().getChildren().clear();
        URL url = getClass().getResource(sURL);
        //this method returns the AnchorPane pContent
        AnchorPane n = (AnchorPane) FXMLLoader.load(url, ResourceBundle.getBundle("src.bundles.bundle", getLocale()));
        AnchorPane.setTopAnchor(n, 0.0);
        AnchorPane.setBottomAnchor(n, 0.0);
        AnchorPane.setLeftAnchor(n, 0.0);
        AnchorPane.setRightAnchor(n, 0.0);
        getContentPane().getChildren().add(n);
    } catch (Exception ex) {
        System.out.println(ex.getMessage());
    }
}
So what basically happens is:
When the program starts, set content pane in the Context:
@Override
public void initialize(URL url, ResourceBundle rb) {
    Context.getInstance().setContentPane(pContent); //pContent is the name of the AnchorPane containing the content
    ...
}
When a button or menuitem is chosen, I load the FXML in the content Pane:
@FXML
private void handle_FarmerListButton(ActionEvent event) {
    Context.getInstance().showContentPane("/GUI/user/ListUser.fxml");
}
Hope this helps :)