Can Iterators be made user-specific or shell-session-specific?

[David Medinets]

I'm asking in case I missed something in the documentation. This issue
hasn't arisen before since I haven't shared tables before. When I attach an
iterator to a table in the shell, it affects everyone (and every process)
that accesses that table. Is there a standard of practice? Do people clone
tables before developing new iterators or before exploring data with
existing iterators?