At least while the person is alive on earth, I believe it is principally sanctifying grace which sanctifies the soul, correct? So, in purgatory something altogether different finishes the process of sanctification? You'll read from St. Catherine of Genoa and others the fire in purgatory is the fire of God's love or something similar. I've heard sanctifying grace referred to as a share of God's life. Could this be this fire maybe? Is the process of sanctification in purgatory done differently than on earth? My thoughts seem to be close to the eastern doctrine of Theosis, althought they also believe that this process never ends for all eternity where I have believed that eventually the soul is "perfect" and then united with God.
I think we are rapidly reaching the point here, if we're not already there, of getting outside our pay grade.
These are the things of mystery and we can't know for sure in this life. I have heard it said before, that we know little more about purgatory, than the fact that it exists.
My understanding is that sanctifying grace cannot increase in the next life, but I'm not willing to dogmatize on this or say anything else with any degree of certainty.