You can usually reapply after 2 years to MBB; sometimes they let you reapply after one year, but they normally mention that in the feedback when giving you the rejection.
In order to increase your chances to get an offer you should:
- Leverage or build a network of consultants in MBB, to maximize the chance of getting a referral when applying again and thus maximize your chances to get a new interview.
- Understand what you did wrong in the case interview and practice on that particular area. Candidates tend to think about cases as a whole thing, but it is likely you have to improve on specific areas, while you may be already strong in others (fit, structuring at the beginning of the case, graph interpretation, communication, math, final recommendation, etc).
- Prepare a strong answer on how you improved since the last interview (they will for sure ask you that question).
At the following link you can also find a recent post I wrote on the main factors that could have an impact when switching from a consulting firm to MBB:
Hope this helps,