Due to COVID Pandemic, most of the colleges have cancelled their entrance exams and are taking admissions on the basis of board %. However, the admissions to NITs/IITs/IIITs will be based upon the JEE scores only. So, if you think that you may get a better percentile and rank in JEE (or have already secured in JEE Main Jan), then you are advised not to apply for other colleges. But if you think that you may not get a much better percentile/ rank in JEE, then you should apply for other colleges now. And in the latter case, if you get a better percentile/rank in JEE later, then you can cancel the admission in any other college you have applied and can go for IIIT/NIT/IIT on the basis of your JEE score.

Hope it helps.