Answer honestly at the level of detail that is useful. You can say you are in a few active consulting processes and mention timing without listing every firm unless you want to.

Recruiters ask partly to understand deadlines and partly to gauge how quickly they may need to move. A factual answer is more useful than trying to sound in demand.

For example: "I am in two other processes at an early stage, but I do not have an offer deadline right now. I will let you know if that changes."

Do not invent leverage. Share real deadlines when they become relevant, and keep the focus on your interest in the role you are discussing. The interviewer should be able to see what you would actually do next, not just hear a general principle.