Every 5 years or so I severely cut back many of my plants that have just plain gotten too big for containers like my Tropical Hibiscus. I always do this in the Fall once the night time temps consistently get below 55 degrees. I cut the tops down to about 4 inches above the soil line and the roots back to about 1/3 of what was there then repot into smaller pots. Since they are stored in a heated greenhouse that is set only for 'don't freeze', I usually start seeing new growth coming from old leaf nodes within 2 - 3 weeks since the soil temperature stays cool. Nodes are not obvious at all, especially on the old growth. On multiple stems, I'll wait until it's clear as to which way the new growth will be growing then prune the plant again to shape it. For example if I have a lot of new growth heading for the center of the plant, I'll remove some of the new stems so the center won't be overly crowded.
It's always kind of scary to do this but I haven't lost a plant yet. Also, it takes about a year for the plant to be back to its old splendor and it's totally worth it on old plants .. it literally does rejuvenate them.