Santa Rosa should be self pollinating, and that should get you more than 3 a year.
When I had Santa Rosa and only that tree for a plum I would set quite a few but they would quickly fall off because of Plum Curculio. They would fall off so small that I didn't even have time to bag them.
Are you spraying?

Find one of the small ones and check it over closely for a tiny crescent shaped hole.

If they don't have any holes then I would think about another for pollination.
Or if you bought this tree at a box store it's possible it's not a Santa Rosa at all.

Methley is probably better suited for your area anyway. Santa Rosa in the west doesn't need a pollinator. My Santa Rosa has always been a very heavy bearer, even when I did not have any other plum trees nearby.

I am one who doubts that pollination is your non fruit problem. Talk to your local county extension office and see what pests or diseases could be responsible. I don't think your trees would be the only ones to suffer. Al

My Santa Rosa produced every year until my native plum died and it has not produced much of nothing since. "Just Fruits and Exotics" the nursery that I have faith in says Santa Rosa needs a pollinator and recommended Methley.
I have planted a Methley this year betting my Santa Rosa will start producing again.