Can a New Plum Tree be Planted where an Old Plum Tree Grew?

The plum tree in the back yard is several years old and is growing well; it is actually quite big.
However, it has never flowered.

It was given to us by a co-worker and I am starting to think it will never flower. Perhaps it started out as a sucker from their tree. (In which case, without being grafted, it probably is only good for root stock.)

I am considering tearing this tree out and replacing it with a brand-new young plum tree from a nursery.

A question before I do this: can a new plum tree be planted where a plum tree grew previously? I read that some trees do not like to grow where a previous one used to be, but I don't know if this is the case for plums.

Any suggestions?

Should I wait another year for the existing tree to flower, or have I waited long enough?

How long is several years and how big is quite big

Do you know what kind of plum and be more specific on age and size?

Janet Reed wrote:Do you know what kind of plum and be more specific on age and size?

Hi, Janet.

I have no idea what type of plum. The co-worker who gave it to us a few years ago is no longer with the company, so I can't ask her.
We've had it at least three years, and it is about ten feet tall. Attached is a photo.

There are also two other plum trees on the property. They were here when we moved here, so they are at least five years old. They were about six feet tall when we moved here.
Again, never seen these two flower either. Photo attached.

Do you do fall pruning?

Janet Reed wrote:Do you do fall pruning?

I ask because bloom/ fruit seems to happen better when we prune back in fall.  Also fertilization has a bearing on fruit trees. I fertilize fall and spring.

I have several plums of 2 kinds.  Some of the younger ones are starts from 2 old trees.  Several are easily 5 plus years old and they’re just beginning to put on fruit and bloom.  And, some years even the old ones have little bloom or fruit.

Can you replace a plum tree with another in the same spot?  I don’t see why not unless there is disease and you’re worried about that.  But I’d be patient, prune and fertilize.

Hi, Janet.

Okay, I'll be patient for a while longer.

No, I have never done Fall pruning. Only Spring pruning; I thought that is the best time to prune plum trees (before they come out of dormancy.)

I'll give it some tree food too.

Thanks for the feedback.

My plum and pluot trees are 4 years old and do not produce yet.  I have one that is 6 years old and only started to produce after I grafted other varieties onto it. I think this was only a survival mechanism since the fruit did not stay.  
Find some scions from trees that are producing fruit and graft them on. I did an Asian Pear and a AU Cherry Plum this spring and had good results and hope to start getting fruit in the next two years.