First of all it is hard to judge for me, why you have been rejected in EU/US, because more information on your CV is required (higher education - university, grades, extra curriculum chievements, etc.), job experience (full time and internships).
Secondly, if you have applied to MBB Middle East right after applying to MBB in EU/US (within less then 12-24 months), you have been rejected automatically. After you register yourself in the HR System of the company your data is stored for quite a long period of time. If you've got rejected, your profile is frozen for the next 12-24 months. In this way each consulting company expects you to further develop your profile in the meantime (continue/finish your education, do additional trainings, get more relevant experience).
Third, of course having some ties or interest in the region is important, but it's not a K.O. criterium, since Middle East offices pretty often hire their candidates from targeted business schools in Europe or US. I doubt that you was rejected due to lack of "Why ME?"-explanation.
My recommendation for you is the following:
- Improve your profile through completing your colleague education/getting additional qualifications
- Or/And get relevant practical experience in consulting (other tier1 or tier2), industry or startup
- Try again after 18-24 months to get into MBB after the above is fulfilled.
I hope it helps.