Is there any bank that will allow to do that?

Actually WaMu has a CD that you can add to. Not sure if anyone else does. But then I don't like WaMu.

Most certificates of deposit are a purchase of the certificate ( your deposit) with a promise of an interest rate for your promise to leave that amount in that account for a certain time frame, The best rates I found today was for 16 months with fairly good rates on 11 months and the lowerr rates on the 4 months. So it is your bet on what you think interest rates are going to do, if you think over 12 months interest rates will rise, then you get a shorter term, if you think they will go down, a longer term.

I was not aware or WAMU but as with Scott I have had some issues with them, so I guess they will base your interest off a promise to deposit a certain amount each month, but in real life, it sounds like nothing more than a savings account with a fancy name for marketing.

Which is what most people do, put money into a savings account, get up to a certain amount then purchase their CD's