SPRAY grill grates with no-stick cooking spray. Heat grill to 350 degrees F to 375 degrees F. Generously season tenderloin with salt and pepper.
MIX blackberry jam, barbecue sauce and seasoning in a microwave-safe bowl. Microwave on HIGH 30 to 40 seconds; stir to blend.
GRILL pork, turning occasionally, 16 to 20 minutes (or until thermometer reads 160 degrees F). Baste liberally with 1/4 cup blackberry barbecue sauce during last 5 minutes of cooking. Transfer tenderloin to platter, tent with foil and allow to rest for 5 minutes before slicing. Serve pork over brown rice, drizzled with additional sauce and sprinkled with chopped parsley, if desired.