You can do a change in terms for checking, savings, money market accounts. Why can't you do the same for certificates of deposit? What is it that makes those specifically different? Asking because even the Wolter's Kluwer generated disclosure we give to customers on CDs states, "We may change any term of this agreement. Rules governing changes in interest rates have been provided. For other changes we will give you reasonable notice in writing..."

Because a CD is a contract for a specific amount and for a specific time and usually also requires the depositor to pay a penalty for early withdrawal. If you could change the term of the contract with me at any time without my permission and then also assess me a penalty if I did not agree with the change - good luck in finding any depositors that will agree to that sort of account.