I just heard in conversation:
Il a été en contact avec elle plus que l’infinie majorité d’entre eux. C'est un privilège en soi.
I assume he wanted to emphasise the idea of "majorité" by adding the word "infini", but this is the first time I have heard this particular turn of phrase.
I usually say "l'écrasante majorité d’entre eux" myself, and I wonder if "l’infinie majorité" works more or less the same way?
Or perhaps, I didn't hear correctly what he said. But a similar-sounding word to "infini" that could be used in this context doesn't come to mind.