Practically, no.
There have been .222Rs made that might could be made to work, but they are rare and expensive.
If you are worried about future availability, just squirrel a few bags. At around $30 for 250, it's the cheapest method.
For the real worrier, if .357 Max brass ever dried up completely, a very minor chamber mod would make the rimless version mentioned earlier workable in those guns whose extraction could be made to handle rimless cases.