computability – Power of a Restricted Turing Machine

The question asks what type of language (normal, without context) a Turing machine can accept if you are not allowed to overwrite the input string. The initial configuration of the machine is the start symbol followed by a blank followed by the input string followed by an infinite blank. The head points to the white just before the input chain. I think this machine can perform all the operations that can be performed by a Turing machine without restriction, because you can first copy the input string to the tape and then continue the operation. However, my friend pointed out that you can not copy the channel without overwriting it at some point. Thoughts?