OP- none of us are telling you that you don’t have the “basis” for an appeal. Anyone can appeal anything.
The issue is are some factors (like high medical costs for a sibling with a chronic disease) more compelling during an appeal than others. And the answer is clearly yes- professional judgement doesn’t mean “anyone who has high expenses will get more aid”, it means "we can- in certain circumstances- override a formula, as long as there is evidence of hardship.
Just make sure you have some options which are affordable. And hope for the best!