it depends on what they need the character to do.
while i don't pretend to work in the workshop, i remember that on elmo's grouchland movie, there was one basic "hero" version kevin used mostly. there were others with bendable wire skeletons for posable shots, one radio controlled version, one with eyes that lit up, even one that dangled on strings like a marionette for one particular shot. and the main figure probably had a spare.
mostly, the main puppet characters seem to be singles unless wear makes it necessary to rebuild. carrol spinney said the oscar he used was an older one that "just seemed to feel and work better", which had been restored. and some of us auditioning for background characters were given an older, retired, "practice" oscar to audition with.
importantly, though, the muppet builders maintained a workshop on the lot so that things could be repaired or created within a very short time. it was not uncommon to see one of the two pros doing some quick "first aid" on a figure with needle and thread between takes.
i'm assuming this was and is standard practice.