Wild idea: The Discovery gets destroyed by some mysterious force in the first episode, the Shenzhou arrives and picks up the survivors, "High Ranking Starfleet Official Guy" tells the Shenzhou to find out what happened since that would be quicker than going back to a Starbase to drop off the Discovery survivors (since they're at the far end of the Federation border). And by "mysterious force" I don't mean some powerful new enemy attacks the ship, more like the Discovery enters a region of space, something starts happening to the systems, ship kerplodes, then there's some sort of energy signal they can trace to a solar system or something, then they try to figure out whats what. Then to keep the show going they introduce a new Discovery in the second season, or perhaps more interestingly they break from the whole ship/station = series name thing and its called Star Trek: Discovery because they're going to go discover stuff.
Highly unlikely I know, but its fun to speculate. And as FLO pointed out, two crews joining has already been done with VOY, and it will be more interesting to see how they pull off this two ship situation, especially if they get roughly equal screen time.