it really depends whether you mean switching from an audit division or switching from a strategy division (eg Strategy&/Monitor/Parthenon) from Big 4 to MBB/boutiques.
If you mean from a strategy division, it is definitely possible to switch as a lateral hire.
If you mean from an audit division, it is not easy to switch directly to MBB. In order to increase your chances you may opt for the following:
- Move first to the strategy branch present in some of the big 4
- Expand your CV with more strategy roles; this could be done working as advisors for a startup, or an NGO
- Develop a good MBB network and use their referrals rather than the online applications only (this recommended anyway even if you are currently in a strategy division)
In case the previous points do not work, you may also consider doing an MBA; this will take more time and money but can increase your chances significantly.