Nested IFS and multiple logical formulae

Ok so this is a tricky one...

I have uploaded a screenshot for reference- Cell J7 needs to the valid discount with three conditions. 1. there is a discount threshold meaning the consumer must purchase at least that quantity to get the discount, 2. "Tom Hanna" is excluded from all discounts, and 3. all T-shirts receive double the discount rate.

I met the first two qualification with simple IF functions as you can see below and in the screen shot.

=IF($A7="tom","0",IF($E7>=$I7,$G7*$H7,"0"))

I can not figure out how to incorporate #3 into this SAME FUNCTION. Any thoughts guys?