There is no predefined way to do this.
You'll probably want to start by defining your own replacement for
overwrite-mode, mirroring what is done for
Switching (for example), the keys for commands
Binding your own replacement command for
backward-delete-char in place of
delete-char in the definition.
However, because there are multiple predefined Lisp functions that use
overwrite-mode (e.g., check the value and do something accordingly), you might just want to advise
overwrite-mode, instead of defining a replacement command.
Finally, I would ask why you want to do this? What is your actual use case?
Update after your use-case comment:
In that case:
M-x picture-mode -- see the Emacs manual, node Picture-Mode and its 4 subnodes.
Maybe try the
table package -- see the Emacs manual, node Text Based Tables and its 8 subnodes.