A lot of plums require a pollinator and even those that are billed as self-fruitful will produce more and bigger fruit if they are pollinized by another tree.

Plums will bloom on old wood, I barely pruned by Santa Rosa this winter and I had a ton of blooms. I do not think that it produced too much fruit, but that's another problem...

They don't bloom on old wood. All blossoms are on wood that grew last yr. However that isn't quit what it sounds like. The small branches and spurs that had leaves last yr will have blooms this yr. Some of those spurs only grow a very small amount but that's enough to set fruit buds. Once a spur quits growing and doesn't produce leaves it won't have flower buds either. Plum spurs are longer lived than apricot or peach but shorter than sweet cherry.