I have a long history on running interviews for BCG and I am happy to share my knowledge to you to be well prepared!
Coaching will be tailor made based on candidates' needs and seniority.
General approach is to run business cases preparation, where structuring well the framework and then drill-it down properly is a key competence to have, in order to pass successfully interviews.
With Oliver Wyman a stronger analytical focus is needed whilst for BCG more logical skills are required.
Also fit interview preparation can be done at the beginning or at the end of the coach, to help candidates best approach to reply well and be successful.