I joined an existing consulting company. There are numerous consulting teams, all with a different focus/mindset.
If you're interested in this type of work you want to decide up front if you're looking to branch out on your own or join an existing team. If your goal is a team then LinkedIn and other such search engines are good options.
I'd also mention that consulting is fluid and if you google companies in your area that do this work they may just have an open entry form for potential candidates.
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