Stemness is a phenotype associated with cancer initiation and progression, malignancy, and therapeutic resistance, exhibiting particular molecular signatures. Targeting stemness has been proposed as a promising strategy against breast cancer stem cells that can play a key role in breast cancer progression, metastasis, and multiple drug resistance. Here, using a previously published one-class logistic regression machine learning algorithm (OCLR) built on pluripotent stem cells to predict stemness in human cancer samples, we provide the stemness index (mRNAsi) of different canine non-tumor and mammary cancer cells. Then, we confirmed that inhibition of BET proteins by (+)-JQ1 reduces stemness in a high mRNAsi canine cancer cell. Furthermore, using public data, we observed that (+)-JQ1 can also decrease stemness in human triple-negative breast cancer cells. Our work suggests that mRNAsi can be used to estimate stemness in different species and confirm epigenetic modulation by BET inhibition as a promising strategy for modulating the stemness phenotype in canine and human mammary cancer cells.