Oh dear, I posted something like this about 3 or 4 months ago. I can now answer as a more experienced jasmine grower. The plant looks good, but if you've had it for a couple of years, its needs are clearly not being met.
To quote robert (who will probably chime in), Jasmine sambac is a BEAST, and it should be at least two foot tall and as broad in two years (or more).
Things required: Plenty of sunlight (at least 3 or 4 hours direct sun per day), frequent feedings, water when dry, warm temperatures (60 to 90F) Stand back...plant growth seems to me to be, flush of new growth terminated with flowers, rest about a month, then flush of new growth from most every node of the last flush, etc. Even back nodes near the soil line are sprouting for me....it's gonna be bushy in there.

I accquired a Maid of Orleans JS in October as a rooted cutting from Logee's greenhouse, and it's bigger than yours in all dimensions, now. That's an indications of what growth is can be like...and should.

Given that, yes, you can prune whenever you wish if the plant has enough reserves to deal with it. Yours might not...since it doesn't grow. And you should be able to make it much bushier. Though, from mine, it seems it'll take care of the bushiness itself, without pruning, though pruning may be required to keep it in check and able to fit back into the house/windowsill next year.

It's wonderful to smell it as I do the dishes (kitchen window...south facing).

dbarron thanks for your detailed response.

I checked MOO, and from what I gathered it is the most vigorous of Jasmines, mine is an unknown species variety.

It was a 2" plant in a 2" pot.
The first year I put it in a big pot, thus there was no growth. Yet it flowered.
It was suggested that I should put it in a smaller pot. That's what I did. And then it started to grow.

I fertilize it at each watering, with foliage pro.

Mine does exactly like yours it blooms, takes a pause, then there are new shoots, but the shoots are at the top tip of the branch.

It's a relatively easy plant to take care of, I'll give it another year and if not satisfied I might get a MOO.....

Hard to believe Jasmine sambac can be that different, it's a selection, not a species ;) if indeed yours is a sambac (it does look like it)

Your comments forced me to check my correspondence with the seller.

Their original plant is It is not a known cultivar but a seed grown plant. Height 10"- 18".
The flower is about 1/4 - 1/2" diameter. They come out with a pink tinge, but mature to pure
white.

I like it besides being my first jasmine, it is small and manageable. From what I've read MOO can become very unruly.....

Well, if you're happy, is what counts, I guess.