But Mr. Galanis’s even-more-valuable intuition was this: Famous people are willing to do a lot more for money than was previously assumed. Mr. Galanis recalled asking the New York Knicks player Lance Thomas, a friend of his from college, how much it would cost for him to make an appearance at a Long Island bar mitzvah, and he replied, “Bro, I’ll go anywhere for $2,000.”

Mr. Galanis did the math: Maybe three hours at the event, plus one hour of travel each way, amounted to about six dollars a minute. But boil an “appearance” down to just the few minutes is takes to shoot a video, and such experiences could be made available on a wide scale — “the greatest gift ever, and cheaper than a ticket to a Knicks game,” Mr. Galanis said. Mr. Thomas is now a Cameo investor and on its talent roster.

Along the way, Cameo has unwittingly created a new style of performance. Some practitioners are more skilled than others. Occasionally, requested messages enter the celebrity’s brain and come out garbled. Others just seem insincere.

Even a “bad” Cameo offers something of value, which is a totally new way of analyzing a celebrity persona. Dina Lohan, best known for giving birth to Lindsay, has struggled to adapt to the form. In her Cameos, she regularly appears perched in a striped armchair next to an enormous silk curtain contraption, filmed from across the room by an unseen handler. Her messages come off as scripted and rote, which, of course, they are. She has received such feedback from users as “She said 31st birthday instead of 35th” and “She doesn’t seem to be having fun.” But there’s also something wonderful about receiving a text message containing an artifact like this. It’s like a direct injection of her arid momager essence.