Children are not usually allowed in, but I'm prepared to make an exception in this case.

儿童一般不允许入内，不过这次我可以破例。

《牛津词典》

Couldn't you make an exception?

你就不能破例一次吗？

youdao

I know it's uncommon to offer a high school student this volunteer job, but I hope that you can make an exception for me, and I'll prove myself.

我知道让一个高中生做这种志愿工作并不常见，但我希望您能为我破例一次，我会证明自己的。

youdao

In the case of Plato, I'm going to make an exception.

对于柏拉图这块,我会做特别对待

耶鲁公开课 - 死亡课程节选

but not that good at other things, you know, they'll make an exception, so.

但是别的不行，他们会破例，就这样。

成绩不是全部 - SpeakingMax英语口语达人

What if we have a case where making an exception and violating individual rights actually will make people better off in the long run?

如果有个特例,侵犯个人权利,长远来看，反而让人们获益更多呢？

耶鲁公开课 - 公正课程节选

He would make an exception for patients who can't take other drugs because of side effects.

FORBES: Magazine Article

The investors seem willing to make an exception for assertive managers such as Mr Welch.

ECONOMIST: Honeywell and AlliedSignal

Kelton said that Vanguard might make an exception if a customer could show different beneficiaries were needed.

FORBES: Is it time to move your IRA?