It has long been realized that symmetry-adapted discrete variable representation for molecular systems with nontrivial symmetry leads to significant reduction of the grid size, and thus computational costs. In this work, we show that even for molecules with no symmetry it is still possible to achieve significant computational savings by symmetry adaptation. The extended symmetry-adapted discrete variable representation takes advantage of the higher symmetry in a part of the total Hamiltonian denoted as the reference Hamiltonian, e.g., a kinetic energy operator. When the evaluation of its action constitutes the more expensive part of the calculation such as in discrete variable representation (DVR) based methods, significant savings may ensue. Applications to several commonly used kinetic energy operators are discussed. Numerical tests in simple as well as realistic systems are carried out to demonstrate the efficiency of the method.