It depends on the "they" you mean here, but some people did make a sequel.

Matt Damon portrayed the brilliant, psychopathic liar Tom Ripley in 1999's "The Talented Mr. Ripley," produced on a $40-million budget and nominated for five Oscars. It was based, as you point out, on a novel of the same name by Patricia Highsmith, the first of five novels she wrote featuring the Ripley character.

The second novel in the series, "Ripley Underground," was actually made into a movie in 2005. You may not have known this, though, because it had a different actor (Barry Pepper) in the Ripley role, and was a much lower-budget, lower-profile affair.

Pepper was going for similar roles to Damon at the time, and indeed they starred together in 1998's "Saving Private Ryan," but he never reached Damon's level of fame.

It gets more confusing from here, because there was actually another Ripley movie made in between. Famed cinematic oddball John Malkovich played the character in 2002's "Ripley's Game," which was based on the third book in the series (despite being released three years before "Underground," based on the second book).

"Ripley's Game" had a pretty big budget -- $30 million -- but was actually a European production and so didn't gain much attention on this side of the Atlantic.

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