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Reporting
If it's grafted (which isIf it's grafted (which is probably the case), the sucker isn't going to grow into the same plum tree. If you want your single plum tree to thrive, clear the suckers so all the energy is put into the tree or it will suffer.

2015 Special Edition Garden GuideCooking Fresh with The Old Farmer's AlmanacThe Almanac Monthly Digital MagazineWhat the heck is a Garden Hod?