You don't have to choose every permanent or player that has a counter, only the ones you want to add another counter to. Since “any number” includes zero, you don't have to choose any permanents at all, and you don't have to choose any players at all.
Urban Daggertooth
If Urban Daggertooth has a +1/+1 counter on it and is dealt lethal damage, it will die before its triggered ability resolves and you proliferate. You won't be able to add a +1/+1 counter to it in time to save it.
While proliferating, if you choose a permanent or player with multiple kinds of counters, the permanent or player gets another counter of each kind, not just one kind. This change from the original proliferate rules was introduced in a previous set.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Randy Vargas
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
