We are considering adding a new tier to our money market accounts. Would this trigger a change in terms for our existing money market customers?

I would say a change in terms is required. The new tier may result in a higher rate for some customers, but could affect some customers negatively if not now, in the future. For example, say the new tier is for balances of $100,000+ and a customer has a balance of $105,000. The new tier may increase the customer's rate, but if you do not provide a CIT and the customer withdraws $10,000 the rate will drop to the lower tier, and the customer would not know why.