there is the Triple Screen test which i think is around 16 to 18 weeks, just a copy from the web below...

...A triple screen is a blood test that measures three things called alpha-fetoprotein, human chorionic gonadotropin and unconjugated estriol. The results of the blood test can help your doctor see if your baby may be at higher risk for certain birth defects such as Down syndrome and neural tube defects...

But google it to get more information.

this doesn't seem as popular here, but when I was living in Namibia pregnant with DD, this is what they offered me instead of the combined blood & nuchal at 12 weeks.

L x