Most plants with a tendency to grow 'viney' are very easy to clone. If you look in the axil (crotch formed by the leaf petiole and the stem it's attached to, you'll probably see embryonic branches which are suppressed by a chemical produced in the tip (growing end) of the vine, like these on the Mexican petunia (not a petunia) being prepared for propagation:
Do you see what look like small leaves in the crotch formed by the leaf stems and the branch? Those are branches.
Prepare the cuttings:
Cut the bottom immediately below a node with a very sharp tool.
A #11 scalpel is only a couple of bucks (drugstore) and it's perfect for taking/preparing cuttings.
The cutting should be long enough that you can bury 2 nodes in the soil and have 1 pair of leaves above but not touching the soil. Cut the 2 leaves in half with scissors but don't take the cutting with scissors. They crush delicate tissue and that's the perfect place for rot to begin. Ideally you would be able to keep the soil damp but never wet or soggy. If you think you might have an issue keeping track of how wet the bottom of the pot is, make sure the soil is at least 6" deep. That is so the basal end (bottom) of the cutting is never immersed in a layer of saturated soil toward the bottom of the pot.
You don;t need a propagating aid, but if you prefer, Clonex is good. Make sure the base of the cutting has no loose debris on it. Shake the container thoroughly with cap on. Open immediately and quickly dip the cutting in the foam created by shaking so the bottom 2 nodes get coated. Make a small hole in the moist medium and carefully insert the cutting(s), trying to make sure the rooting aid remains stuck to the cutting and doesn't rub off on the sides of the hole. Gently settle the soil around the base of the cutting (a bamboo skewer works well) and tent. Keep in bright or open shade. Roots should form within a week.
2 branches/vines will grow from the crotch of the 2 leaves. When each branch has 2 leaves, pinch the branches/vines - that will give you 4. If you want the plants really full, pinch again so you'll have 8 vines from 1 plant.
Al