Yes you can. However like keith said pairing up random sticks of RAM can sometimes not work. To reduce the possibility of this try and buy the exact same brand, model, specs that you have already. Please also remember your RAM can only run as fast as your slowest RAM stick, so since you have 1600 don't bother buying sticks that are faster than that.
Personally I haven't had a mixed stick problem in a long time so your chances of it working are greater than your chances of it not working. Its just very annoying when it doesn't work as each individual stick works fine, just not together.