It's known by other names as well, but the correct botanical name is Schlumbergera, of which there are (at least) 6 recognized species. So my first thought is that you should first of all identify which one of those species it is so you can study up on that particular species and determine exactly what it's unique needs and habits are, and what kind of soil (medium) conditions it requires to flourish. Here is some information to get you started on researching the individual species so you can try to identify your particular plant by its appearance and observable characteristic:
https://en.wikipedia.org/wiki/Schlumbergera
More to the point to address your specific problem though, the schlumbergera plants are what are known as
short day cycle plants. That means that in order for them to set blooms, short day cycle plants need a decrease in light for a certain period of time, and long day cycle plants need an increase in light. So if you want yours to stop blooming and encourage it to start growing new foliage instead then you could try tricking it by
increasing the number of hours of daily light that it gets.
Don't cut off the blooms, let them expire naturally, but I would suggest that you introduce artificial lighting in order to increase its daily dose of light conditions to 18 hours per day until it stops blooming and starts growing new foliage. Don't give it too much direct natural sunlight because the UV will burn it. Keep in mind that they are classified as epiphytes because in nature they grow in shady areas up in the tree canopies, not in soil on the ground in direct sun. Once it has grown more foliage that meets with your satisfaction you could gradually start decreasing the light conditions again back to what would ordinarily be the more natural light requirements it needs under more normal growing conditions.
However, I'll caution you to not trick it for too long within the year, to eventually let it do what it wants to do, otherwise you might weaken and make it sick from preventing it from growing in accordance with its natural inclinations. It's never a good idea to trick and go against Mother Nature's designs for very long periods of time.
Here is some additional information about what makes schlumbergera plants 'tick' and what their normal environmental conditions and light and temperature requirements would be. Now the site is about how to get the plants to bloom but you can use the information to figure out how to get the plant to do the opposite of setting blooms:
https://www.canr.msu.edu/news/the_se...ture_and_light
If you try that I'd be interested in seeing your update in this thread at a later date when you know what the results are. I've done this kind of 'trickery' with other plants and other epiphytes but never with schlumbergeras.
Images of schlumbergeras:
https://www.google.ca/search?q=Schlu...w=1117&bih=541
.