Cut the top off a thick, healthy stem on the Poet Jasmine, leaving 3 to 6 inches of stem. Make a cut across the stem at a 45 degree angle. This plant preparation is called a root stock. The remaining upper plant material will be removed later after the graft union has joined.
Cut the top off the other jasmine species at a slant that is identical to the angle that you made on the Poet Jasmine. The two surfaces will need to match and fit together. Discard the base of the plant. You will be using only the top, called the scion.
Slide the two pieces onto each other with cut edges touching. Wrap the union together using several layers of grafting tape. Bury the graft union with peat to prevent it from drying out.
Place the pot with the grafted plant on an open bench at a temperature of 65 to 75 degrees Fahrenheit for four to six weeks. Cover the entire plant and pot with a clear plastic bag. Remove the bag once a day to air the plant and prevent rot at the union.
Use a plant mister to moisten the soil and keep it moderately damp. When you see the union has callused and knit together, remove the plastic and cut back the remaining stems on the rootstock halfway. Continue warm temperatures and moisture for six more weeks. Remove the remaining rootstock stems.