You can try Aventuras Tierra Adentro http://www.aventuraspr.com for a custom adventure. I went with them on a cave trip many years ago and it was amazing. Another good company is Acampa Puerto Rico http://www.acampapr.com . There is a private rain forest on the central/south part of the Island called Las Casas de la Selva http://www.eyeontherainforest.org . It’s not a place for extreme adventures but hiking trails are nice. You can stay there in a tent or in a guest house. Service is limited so you’ll share restrooms and eat whatever they’re cooking that day.