computability – Power of a restricted Turing machine

The question asks what kind of languages ​​(regular, without context) a Turing machine can accept if it is not allowed to overwrite the input string. The initial configuration of the machine is the start symbol followed by a blank space followed by the input string followed by infinite blank spaces. The head points to the blank space just before the input string. I believe that this machine can perform any operation that an unrestricted Turing machine can, since it can first copy the input string on the tape and then continue with the operation. However, my friend pointed out that you can not copy the string without overwriting it at some point. Any ideas?