Put the crab meat in a bowl and add the saltines. Beat the egg yolks, then pour them on top. Add the remaining ingredients and gently fold everything together, being careful to not break up the crab pieces too much.
Use an electric mixer to beat the egg whites to soft peaks, then gently fold this into the crab mixture.
Shape the mixture into 3 ½" rounded cakes.
Fry in a heavy bottomed saucepan in a mixture of butter and olive oil over medium-high heat until lightly browned on both sides. Be careful not to overcook.