If you find that you are short on points with AA, you can always purchase additional points.

I second the suggestion to use expertflyer.com to first find an AA flight with availability before you call to use points to upgrade. For any domestic segments you need A inventory to use miles to upgrade. For any international segments, you need to find C inventory. There is an award search feature on the site which shows that.

You could also just try to find the SAAver award seats searching on aa.com. If they exist for award, then they should be available for upgrade with points.