We’ve thought about adding multiplayer features to Zombies, Run! pretty much since we came up with the idea over three years ago! That means we have a very long list of ideas at this point.
For now, we’re more interested in co-op features rather than directly competitive features, and that we think asynchronous multiplayer is probably an easier and more popular route to take first. It would be cool if you could run with friends while hearing the same story — you can sort of do that now providing you have the same playlist and you turn chases off — but given that most runners and ZR players tend to run on their own, synchronous multiplayer is likely to be a bit further off in the future.
That said, we could come up with an awesome idea tomorrow that completely contradicts everything above, so who knows!