Applying new caulk over the old caulk can be done, however it is extremely NOT recommended as it may result in water infiltrations and water damages.    When you caulk over another sealant, the two will eventually  separate from each other. Upon separation, the old caulk situated under the new layer of caulk will continue to get older and may continue to crack, thus eventually allowing water and air through.   For airtight and watertight joints, the old sealants should always be removed and the surfaces should be cleaned before the application of the new sealant. To learn everything you need to know about caulking click on this link