I think part of the issue you will encounter (or are already encountering) is the Anywhere (Europe/Asia) - US saver reward inventory. In most cases you will only see the standard award levels come up. You can certainly use the multi-city function. You will be able to see, for example, SGN-FRA on saver economy or even saver business but then the FRA-NYC leg is only available at the standard level.

It is entirely possible that the saver levels will open up at some point but this is also summer travel so who knows. Good luck.