MBA grad with 4yrs workex. Stuck at an MNC

Hello All, I'm looking for insights from mba grads who are currently working in different sectors of management consulting. Can you help me with the preparation plan and the companies to target?

About me: Baby IIM grad with 4 yrs of total workex. Working as a supply chain consultant in an MNC with a pretty much basic package. I'm trying to pivot to core consulting (can be in SCM, strategy, sustainability) I'm seeking help from people who have gone through the same hurdles and doing well professionally or from someone who tested waters and got a grasp of the situation.

I deeply appreciate any support or suggestions in this regard. Cheers!!