2 hands
I have played two hands at a couple different casinos. The one casino allows you to play two hands unless a person who isn't playing wants to play that spot. They deal the hands, and cover the second hand with a plastic "waffle" as they call it. Once you look at your first hand and bet or fold, they then move the waffle and you are allowed to look and bet on your second hand.
The other casino's 3 Card Poker game is dealt pitch. After the cards are dealt, you can look at one hand, bet, then look at the other. This is a very laid back casino, and they don't say anything as long as you don't appear to be trying to touch both hands simultaneously.