You need not take any extra burden but make sure to appear at least twenty mock tests of AIEEE before the entrance. And all these tests must be done after JEE gets over
It's essential to maintain your study rhythm after JEE so an alternative would be to do group study as the mind becomes too saturated to sit alone and study after giving JEE.
There are some topics that are there in AIEEE but not in JEE
Maths: Statistics, Negative Index series in binomial, Mathematical reasoning
Chemistry: Environmental Chemistry
Focus more on these and also have a look at the practicals given in the AIEEE syllabus. Questions from practicals are straightforward and its important to go through them as most of the students (including me) rarely paid importance to practicals done in their school.
Last, but not least solving previous years papers is really beneficial as few questions exist in the paper that are repeated from previous years questions.
Dont take AIEEE lightly even if you have given your JEE well. The only thing that makes the difference in AIEEE results is the study of these miscellaneous topics after JEE.