Place potatoes in a large pot of generously salted water; place over high heat and bring to a boil. Cook until potatoes are just tender, about 20 minutes. Drain and rinse with cool water to stop the cooking process; when cool enough to handle, cut into bite-sized pieces and place in a large mixing bowl. Add the drained olive salad, ham, salami, and cheeses; toss gently to combine. Add reserved olive salad oil to taste and; serve at room temperature.
Makes about 12 servings.

Note: It doesn’t hurt at all to microwave individual servings for a few seconds to begin to melt the cheese!