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To make this nice and short – No.
It’s like asking someone if you can over learn anything. However saying this, there is a point where you can know so much grammar that you are too afraid to use it in case you get it wrong by accident, or you sit and listen to yourself speak when you are trying to speak naturally, you end up sounding like a robot.
The ultimate goal of any English learner is to become fluent, and fluency is never something that comes easily, it only comes from hours of usage. The more you use your English the more fluent you get.
So don’t be afraid to learn more than you need, English is the kind of subject that will decrease in size if you are heavy handed with it, it will only increase the more you read, listen, speak and write.
One thing to always remember though is to make sure you are learning ‘evenly’ all the disciplines. Don’t spend all your time learning the grammar and not speaking or speaking every day but not bothering with learning the correct grammar. Balance is something to be more interested in than ‘over learning’.
So get out there and learn as much as you can, ‘over-learning’ is something you need to aim for, so long as it doesn’t make you lose confidence or slow you down.
What do you think?