I have known several people who joined a BCG Paris after having work for a few years in other consulting firms (either top 20 or boutique/specialized)
Evaluation criteria during cases interviews will remain roughly the same. Of course they will expect more maturity. They also keep track of previous interviews so they will expect to see significant progress on the weakness they have seen in your first interviews. HR are usually willing to help and explain what went wrong, so be sure to understand that thoroughly. Call back the HR if needed.
However, to make MBBs interested in your profile again in a few years, I would advise you to get experience on the sectors where MBBs have needs.
In BCG Paris, there are a lot of financial services / IT / digital cases. Bain Paris works a lot on M&A…
So, if you acquire experience on insurance or digital in banking while working at your top 20 consulting firm, BCG will be more interested in your future application, than if you work for the public sector for instance.
Also, when recruiting « lateral hires », MBBs tend to divide by 2 the experience you have. So if you work for 2 years in another consulting firm, you will be hired in the same position as someone who worked for 1 year in the MBB. Considering this, I think that 2 or 3 years may be a good time to re-apply, especially if you got promoted in your firm to prove your progress.
Hope this help!