Only one playthrough if you use a back-up save (USB or PSN) - there's an achievement for each of the 3 endings, so without that it would mean going through to the end of NG++Also how many playthroughs are required to platinum the game? The difficulty of the chalice dungeons always put me off going too far into them, but now the population is booming I might go for it.
You need to remember not to consume any umbilical chords for this method, as one ending requires you not to use them, so back-up save before using them