a two-year black list period is pretty common for most consulting companies; you can definitely contact the consulting companies who rejected you though, to verify the exact period with them. I don’t think it makes sense instead to reapply immediately after a rejection with just an improved version of your CV.
As for unanswered and future applications, quoting a previous post I wrote, besides polishing your CV I would recommend two things:
- As also mentioned by Tobias, you may call the recruiter at the office and ask for the status of your application if they do not provide feedback after one month (in my experience that should be a sufficient time). This will not give you any negative result, while could be beneficial in some cases. As an example, after my application at Oliver Wyman initially I did not receive any feedback. After approximately one month I called the recruiter and asked which was the status of my application. She looked at my CV while we were talking over the phone, she liked it (it sounded she actually never saw it before) and invited me on the spot for an interview. In the end I received an offer from Oliver Wyman, and I am pretty sure that if I would have not called them that day I would still be waiting for a reply.
- You can try to find a referral for your future applications to help you in the process. This will allow you to increase the chances to receive an invitation for an interview and also to have someone in the company that may follow up HR asking for news in case they do not provide feedback on the application process. There is a specific method to receive a referral, even when you do not have any current contacts in a firm. The steps are:
- Identify who are the people who could more easily help you
- Write them a customized cold email
- Have a call with the consultant, and indirectly ask for a referral
Each of the previous steps should be structured in a proper way to maximize your chances of moving to the next one; I applied this method, and managed to get six invitations out of six applications from McKinsey, Bain, BCG, Oliver Wyman, Roland Berger and Strategy&.
Hope this helps.