1. Place steak in large resealable plastic food storage bag. In small bowl, combine soy sauce, 1/4 cup orange juice and ginger; pour over steak. Seal bag, turning to coat steak with marinade. Refrigerate steak, turning bag occasionally, at least 8 or up to 24 hours.
2. Drain pineapple, reserving juice. Combine remaining 1 cup orange juice and pineapple juice in 1-quart glass measure; add enough water to make 2-1/4 cups liquid.
3. In medium saucepan, combine juice mixture, allspice and salt to taste. Bring to a boil; stir in rice. Cover; reduce heat to low and simmer 20 minutes. Remove from heat and let stand, covered, 5 minutes.
4. Meanwhile, remove steak from marinade; discard marinade. Grill steak 7 minutes on each side over high heat for medium or until desired doneness. Cut steak diagonally across the grain into thin slices.
5. Place rice in serving bowl. Stir in pineapple and oranges. Serve with steak.
Serving Suggestion
For an authentic Caribbean touch, add 1 cup diced peeled mango to rice with pineapple chunks and oranges.
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