Personal injury lawyers take contingency cases. Employment law is usually hourly.
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Yes many operate on a contingency fee basis if the case is strong enough. You can try to find one through NELA. See link below.
My answering this question does not form an attorney-client relationship. Always retain a qualified attorney before taking any action. My office offers free consultations. www.jrandolphlaw.com
Depending on the strength and weaknesses of the case, an employment attorney might take your case completely on contingency. Our firm does this on a limited basis.