There are a ton of dual core LGA 775 processors. Some quad core ones too.
But, not all will run on the motherboard. Unfortunately I don't know what the max processor is for that board. I'm just cautioning you, so you don't go buy a quad core LGA 775 and stuff it in there expecting it to work.
I quickly googled it and gave up because I find it frustrating to deal with OEMs. The reason is because, as in this case, they brand a computer one name like Optiplex 280, but then they have multiple hardware configurations. That is really irritating when trying to find hardware information.
I don't know if I'll post back in this thread. But if you posted with what processor you have in there now (something like CPUID will be very helpful here) and any information about that motherboard, that would be very beneficial to anyone trying to provide you more advice.