Former Rep. Henry Waxman, who has tangled with industries including Big Tobacco, Big Coal and Big Pharma, thought his congressional experience would position him to help a large law firm advise corporations.

As his retirement from Congress neared, he wrote a business plan, sent it to public-policy group managers and talked to peers who’d preceded him in private practice. A lawyer before he entered Congress 40 years ago, Waxman believed he could “give good counsel to people who have issues that I could help them think through.”