能…了 / 会…了 / 不想…了 / 应该…了【néng…le / huì…le / bù xiǎng…le / yīnggāi…le】

A modal verb – 能, 会, 想, 可以, 应该, 可能 – never takes 了 itself. 了 goes at the end of the sentence, and what it adds depends on the modal.

Can now: a new ability or permission

With 能, 会 or 可以, final 了 says the ability or the permission is new: before, no; now, yes.

• × 我会了开车 → 我会开车了
• × 我能了去 → 我能去了

With 想, it says the wish has just arrived: 我想回家了 "I want to go home now".

Not any more

不 + modal + verb + 了 says something that was true has stopped: a wish that's gone, a plan that can't go ahead. 我不想去 is "I don't want to go"; 我不想去了 is "I've changed my mind".

Should have, may have

With 应该, 可能 and 大概, final 了 makes a guess about something that has probably happened by now.

应该 + 了 can also mean "it's time to". Context decides which.

Not on the main verb either

Something you want or plan to do hasn't happened, so 了 doesn't go straight after the main verb.

• × 我想买了一本书 → 我想买一本书
• × 明天我要去了北京 → 明天我要去北京

要…了 and 快要…了, "about to", are a separate pattern with their own point.