Want to trim phoenix Roebelenii Pygmy Date Palm
It has 4 branches/trunks and I would like to remove one. Will this harm the plant?
There is a possibility that cutting of one stems low on the plant will open it to a soil borne fungus disease: Gandoderma butt rot. This disease is more prevalent in Florida because of the number of palms and increased potential of exposure.
This is more of a risk for an outdoor plant in the ground, than for an indoor or patio plant in a container. If you planted in native soil with other palms in the vicinity, then that increases the risk. If you planted in an artificial growing medium, potting soil, then the risk is minimal, but not impossible for the palm to become infected with the pathogen.
I'd say don't do it unless you have to.