There are such things as wild plums. Have you ever tried planting some of the fruit or taking cuttimgs. Use the rooting compound for woody cuttings if you do.

Are there little ones near your existing bush. Careful looking may net you some plants.

Though the plums are no good to eat, so you say, they may make lovely jelly. I make Jelly from sandcherries which taste gritty and sour from the bush, but made the best tasting jelly I have ever tasted