@Robin *********
IF you actually have a "visa on arrival" it cost you 2000baht when you stamped into the country and was for 15 days only the answer is NO you cannot extend it.
Now if you're just not dialed into what stamp you got when you came here and IF you actually showed up here without having bought a visa from a thai consulate before hand and were stamped in for FREE for 30 days you have a 30 day visa EXEMPT entry stamp and that you CAN extend for 30 more days at the immigration office