From Skin and Haircoat Problems in Dogs
, Lowell Ackerman DVD DACVD, ISBN 0-931866-65-0
Pilomtrixomas are benign tumors originating from specialized hair-forming cells. They usually occur singly and may be found on the shoulders, back, flanks, or legs. Kerry Blue Terriers and Poodles appear to develop them more often than other breeds. Diagnosis is made by biopsy and surgery almost always takes care of the problem. Rarely, malignant varieties do occur.
Has your dog had multiple, separate nodules removed? If so, have they all
been sent for path exam and histologically confirmed as pilomatrixomas? Bassets are also prone to the formation of "sebaceous" (epidermal inclusion/keratinous) cysts, which are benign and which can be numerous. Is it possible that perhaps your dog has had both types of nodules?
In any case, as long as there isn't evidence of metastasis (spread to other organs, like lymph nodes, liver, spleen, lungs, bone, etc.), I'm not sure why your vet would make a recommendation to euthanize your dog.