Place the beef in a deep container for marinating. Add 2 cups Dr. Pepper and the remaining ingredients and mix well. Add more Dr. Pepper to cover. Seal and refrigerate for at least 5 hours or overnight.
Preheat an outdoor grill to medium. Place the tenderloin on the grill, reserving the marinade, and cover the grill (or heat a grill pan over medium heat, add the tenderloin and cover loosely with foil). Cook, turning occasionally, until the meat registers 130 degrees . on a meat thermometer for medium-rare, about 45 minutes. Transfer to a board to rest for 15 minutes.
Meanwhile, bring the reserved marinade to a boil in a medium saucepan, then lower the heat and simmer until slightly reduced, 5 minutes. Slice the beef and drizzle with the Dr. Pepper sauce.