Are there mulberries other than the white and the red?

Our house (in MA) came equipped with a huge mulberry tree -- much taller than the house, maybe 70 or 80 feet. The leaf forms match your photos, and the fruit look similar to the ones in the photos above, though a greater percentage of them are purple-black when they are at their peak of sweetness. But this is no apple-sized tree.

And it produces thousands of babies each year ...