have been 后接形容词时，完全可以连用表示次数频度状语（如 twice, three times, four times 等）。你的以下句子是完全对的：

He has been angry three times today. 他今天生过三次气了。（有过三次生气）

He has been ill three times this month. 他这个月生过三次病。（有过三次生病）

另外，再补充几例：

He has been sick several times today. 他今天吐了好几次了。

He has done well to pass his exams, seeing he has been ill a lot. 考虑到他常常生病，他考试都及格了就很不错。

I don’t want to make a (big) thing of it but you have been late for work three times this week. 我并非想小题大做，但你本星期上班已迟到三次了。