I'd really like to make this work if I could, but I suspect it's impossible in my specific case: all the robocalls I get are scam calls, trying to sell me credit-score services which presumably don't exist. Is it likely that I can get a company name out of them, or that there is even a company to sue?
(And since they are criminals anyway, they have no incentive to settle with me, since even if I win I'd never be able to collect.)
There's actually a decent chance it's a real company. I once got a call for insurance that I was sure was a scam, but after playing them along for several calls, I found out it was a legit company. I talked to their CEO, who was very nice, found out their company name, and then explained to him that I could sue him for several thousand dollars. He apologized, said it was an outside firm that they had been working with, and said they had stopped working with that company because of complaints. I didn't sue them.
(And since they are criminals anyway, they have no incentive to settle with me, since even if I win I'd never be able to collect.)