"This sparked a conjecture that by the <u>end of the inflationary period, there wasn't one universe</u> – the one we see – but a potentially infinite number (the multiverse)."
In eternal inflation, the "inflationary period" only ever ends for patches here and there. Most of the "universe" remains perpetually in an inflationary state. That's Hawking's "fractal-like multiverse".
What you imply is lots of patches of universe side by side functioning as different universes. That can't happen. The universe can't exit inflation "simultaneously" and get different laws.
But I did read a related paper the other day which said that, if you get the numbers exactly right, you can get all the universe to exit inflation and be left with a cluster of different universes. But the "inflationary period" ends at different times and it needs detailed fine tuning; most models tend to produce run-away inflation or a single universe.