Here is the context: 我于是去了这家餐厅，点了一盘蘑菇菜心，果然好吃。我对服务员说: 我再次要一盘。
The sentence "我再次要一盘" is wrong. But "我再要一盘" is correct. Can anyone explain why?
The answer by Camila Ting Chen is close. We don't use 再次 in an present active sentence. We use 再次 with some perfectness or passiveness. Such passiveness is not necessarily related to the conjunctive 被 however. A simple rule is when we can say 再 alone, say it alone.
这盘菜再次被我吃掉了。 while this sentence is not logical at a first glace, it sound good in this specific situation.
我再次要一盘 is "I want the dish again."
我再要一盘 is "I want another one."
It's one of those things that you can say it and people would know what you mean. But it just sounds off.
我再次要一盘 should exist in 陈述句
我再要一盘 should exit in 祈使句
As you are asking the waiter, it's 祈使句.
When the 再+ verb, normally, we dont use the 次. Let's look the sentence again， “我再要一盘”， here “要” means want， is a verb，so, just use 再+verb. If you say: “我再次要一盘”， weird, but not wrong, we can understand.