Here are a couple sauces to try. Have you experimented
with adding horseradish to a bottled steak sauce?

Betsy

Steak Sauce

Blend together:

1 tablespoon prepared horseradish
3 tablespoons catsup
1 tablespoon Worcestershire sauce
1 tablespoon lemon juice
Dash of Tabasco to taste

Hop's Steak Sauce

Mix together:

2 tablespoons brown sugar
2 tablespoons mustard
2 tablespoons hot horseradish
1 cup onion, chopped in blender
2 tablespoons garlic juice
2 tablespoons Worcestershire sauce
3 drops Tabasco
2 tablespoons oil
Juice of 1 lime or lemon
Salt and pepper

Use to baste steak while grilling