Usually you would only say "me gustarían trés sangríaS".
or in English.. "I'd like three sangrias" If you are the one who will drink all three of them !
You would most likely ask for a jug though :P "me gustaría una/media jarra de sangría".
Anyway, If you are not gonna drink them all "trés sangrías por favor" would be more native-like.
Note:You would only Not add an "s" at the end of a plural if you asked something by it's brand (sometimes).