If you loved Friday the 13th Part III, try The Texas Chainsaw Massacre: The Beginning
A bridge between a film you've already seen and one most people haven't. Here's what they share, and what the second one does that the first one doesn't.
You already loved

Friday the 13th Part III
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The Texas Chainsaw Massacre: The Beginning
What they share
Theyboth carry the dread mood tag, and they sit in Horror / Thriller territory. If that's the register that drew you to Friday the 13th Part III, the second film will land in a comparable space — through a different lens.
dread
What The Texas Chainsaw Massacre: The Beginning is
Rural Texas, summer, a crashed car. A group of friends on a road trip, bikers, and a lawman converge, leading to the Hewitt homestead. Liebesman resurrects the horror of a notorious family.