Suppose I wanted to use a character’s morph as a starting point for another morph (in order to alter features or improve expression.) Is there a procedure for doing this sort of thing? I tried importing a morphed head from an exported character, but when I applied the morph the head exploded.

The head exploded because your vertex order got jumbled up.
Did you have more then one group involved? If you did, welding things into a single group, then regrouping it back often changes vertex order.
UV mapper has some tools that can aid with this.

It didn't have more than one group. It was merely a character's head morph, originally created by spinning the morph dials, combined with Poser 7's morphing tool. I just wanted to see if I could import the character's head morph into the default figure's head. Maybe things would work if I checked the "correct vertex order" box...

Nope, it still didn't work. The head just crumbles into a thousand peices.

What figure and what exact steps are you taking?  Don't skip anything, be as detailed as you can (e.g. list the "morph" dials, because not all head dials are actually morphs, some can be ERC dials that scale or translate).

It could be the way you exported the OBJ from Poser or from the app you used to morph with that jumbled up the vertex order.
Hard to know what happened without knowing more detail about what you did... exact steps and setting you used.
Conceptually, you should be able to do what you're doing, but there are a few little intermediate steps that could cause jumbled up vertices.

This is a case where I posted too soon. Rather than list the whole slue of morph settings, I decided to experiment a little more first and had better luck. The time things exploded, I had exported an entire figure before isolating the head in Lightwave for the Poser morph import. This time I merely exported the morphed head and the morph loaded without an explosion.

The problem may be scanners.  If you ever saw the movie, those scanner people could make people's heads explode.  Have you crossed a scanner?