Yes, you may change employers under the Live-in Caregiver Program. However, you must first sign an employment contract with your new employer so that your new employer may apply for a Labour Market Impact Assessment (LMIA). After Employment and Social Development Canada issues a positive LMIA, you must apply for a new work permit.
There are several other steps you must take before you change employers, including asking your current employer for some documents. For more information, see Changing Jobs.