Hmm. If there isn't a built in feature to move the colliding vertices, I wonder whether a Python script could be written to do the job? There's a Python script which "inflates" an object or figure. If the collision detection can be accessed via Python, maybe something similar to the "inflato" function could somehow be used to displace the colliding vertices? Hmm. Dang, I wish I could program.... Hmm.

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Cage can be an opinionated jerk who posts without thinking.  He apologizes for this.  He's honestly not trying to be a turkeyhead.

Cage had some freebies, compatible with Poser 11 and below.  His Python scripts were saved at archive.org, along with the rest of the Morphography site, where they were hosted.