Why more sticky? Do you feel like your bike has a problem cornering? Do you feel like you are sliding out?
You can get grippy tires, but they tend to be more geared to racing and tend to use a softer rubber compound that wears faster and is more flat prone than a more all around tire. Personally I prefer middle of the road for my commuter. Not racing slicks, but not super tough tires like Gatorskins (the ride feels really harsh and slow to me). I've had good luck with vittoria rubinos. The ride is pretty good and they are flat resistant.