This is a topic which I frequently discuss with my mentees. Indeed, it might make sense to adopt an approach which follows several "stages". The following strategy has proved to give outstanding results in terms of MBB offers:
1. Concentrate on proper preparation with excellent case partners/experts (several weeks)
2. Make sure your written applications (CV, cover letters, referrals) are on point!
2. Once you feel really comfortable on fit, cases and your application, apply to several Tier2 firms
3. Continue practicing cases!
4. Schedule interview days with the Tier 2 firms that get back to you
5. Once T2 interviews are scheduled, apply to MBB
6. Continue practicing cases!
7. Go through T2 interviews and get used to the setting (if you focused your preparation on MBB, you will realize that interview formats and cases might be a bit different at T2 firms, but don't get irritated by that fact). Try to get at least one offer (this is a great psychological help!)
8. Schedule interview days with the MBB firms that invited you
9. Continue practicing cases!
10. Nail interviews with MBB firms and celebrate your offer(s)!