How do I change the language of the man pages on Debian, while keeping the default language as english

I've tried changing the man pages on debian from English to Italian but all I have tried hasn't worked yet. First of all, I installed the manpages in Italian with apt install manpages-it. I then edited the /etc/locale.gen file and uncommented it_IT.utf8, then ran locale-gen to update it. After that I tried with:

man -Lit printf
man --locale=it printf
LANG=it_IT.utf8

but none give me the manual pages in Italian. The only manual page in Italian I can get is man man, but the other manuals are just in English.