A picture would be useful.

Perhaps the neighbors know. Ask.

Tree overall

Close up of reddish leaves with tiny fruit (these branches had showy hot pink flowers)

Greener leaves with developing fruit - these branches had pale pink flowers

Trunks at the bottom. Taking this photo, I noticed some suckers of the reddish leafed variety (with small fruit). Does that mean it's probably the rootstock? Does this rootstock growth look way too established to bother trying to cut it back?

Also, the only info the neighbors were able to provide was that their kids picked and ate a small hard apple that didn't taste very good the year before we moved in. But they aren't plant people - in fact, they told me they picked it from the black cherry sapling that I cut down (so they didn't even have the right tree). So who knows if the apple was ripe. Other neighbors aren't of any more help... either too new, or not plant people. Or both.

From the looks of it I would say the red colored growth is very likely the root stock. The Budagovsky (B9), (B118) all have that typical coloration. Looks like the far left and possibly the far right trunks are root stock from the picture. I am sure you can tell from the leaves. I would go ahead and remove those 2 trunks now. IMO I would leave the "regular" apple now and prune out a trunk or two next dormant pruning. I would not rip out the tree and start over looks to be healthy and it can be pruned into a more productive tree if you like the taste of the apples. Otherwise you can graft it over to something else.

Thanks! That's what I was hoping to hear. I'll move along with your recommendations...

One more question. Is there a disadvantage to having a multi-trunked tree? I've cut back the rootstock and I am left with 3 trunks of the fruiting tree. Is it better for the vigor of the tree to cut back to 1 trunk when dormant, or is this just a matter of aesthetic preference? Thanks!

You can leave 3 trunks, [of the good apple] if you have room and prune it so sunlight gets in, or you can graft a couple over, then you have 3 cultivars... more work, for your yard and don't want to graft I'd probably go with single trunk... you can cut all now.