Doing any course is allowed till you starts the articleship of CA. Once it starts only one course at a time is allowed alongwith CA and the same should be informed to ICAI in Form 112.
and the training in cs will also be substituted by CA training, saving of 24 months...
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I suggest to fully focus on CA without opting any other things...Because CA will provide you all plateform and at the last only you expertise will help you so try to clear CA at the erliest..