I think as a repeater you are going to have many issues. First that comes to mind is the rim dragging inside the magazine and trying to hang up. Second will be the shorter OAL of even the smallest cartridges that will feed up the Savage feed ramp from a magazine. And 3rd is the shorter brass will probably not stay on the extractor long enough to clear the action and allow for a 2nd shot.

The 221 Fireball is an example of a cartridge that people try to get to feed in a Savage 10/110 series and normally fail to get it to do so reliably. Often times to get the 221 to run at all it has to be a single shot with the ejector removed. The 357 Max is shorter than the 221 so all of those problems will be even harder.

All that said, if you can spare the funds to try it, by all means do and share with us how it worked for you. Worst case scenario you end up running it as a Single shot if it doesn't work out.