We report on the modification of mechanical properties of breast cancer cells when they get in contact with other neighboring cells of the same type. Optical tweezers vertical indentation was employed to investigate cell mechanics in isolated and contact conditions, by setting up stiffness as a marker. Two human breast cancer cell lines with different aggressiveness [MCF-7 (luminal breast cancer) and MDA-MB-231 (basal-like breast cancer)] and one normal immortalized breast cell line HBL-100 (normal and myoepithelial) were selected. We found that neighboring cells significantly alter cell stiffness: MDA-MB-231 becomes stiffer when in contact, while HBL-100 and MCF-7 exhibit softer character. Cell stiffness was probed at three cellular subregions: central (above nucleus), intermediate (cytoplasm), and near the leading edge. In an isolated condition, all cells showed a significant regional variation in stiffness: higher at the center and fading toward the leading edge. However, the regional variation becomes statistically insignificant when the cells were in contact with other neighboring cells. The proposed approach will contribute to understand the intriguing temporal sequential alterations in cancer cells during interaction with their surrounding microenvironment.