Merge overlapping vertices of different objects The array modifier has an option to merge the overlapping vertices of two segments. Is there a way to do this with the overlapping vertices of two separate objects?

One advantage of this feature with array modifiers is that it allows other modifiers below in the stack to work on a contiguous mesh with no splits. 

In the picture below, I have 3 objects that make up a single whole: two arrayed objects, and another to transition between them. They need to remain as separate objects because they have different modifiers. But the splits where the objects' vertices overlap interrupts the subsurf modifier, creating artifacts like the one circled.
The start and end caps of an array can themselves be 'live' (unapplied) arrays.



If 'merge' is checked in the array modifier, the start and end caps merge with the arrayed object.

So you can apply the array modifier to your transition object (no repeats) and set your first array as the start cap, and your second array as the end cap of your transition 'array'.