Proliferate's rules read as follows:
Choose any number of permanents and/or players, then give each another counter of each kind already there.
So note here as emphasized above:
- It's the permanent/player that is being chosen, not the counters on the permanent/player.
- It's a counter of each kind already there.
So the creature he selected only had one kind of counter on it (+1/+1 counters), so it would get one more +1/+1 counter, not 3.
If it happened to have some other kind of counter (say, a feather counter), it would get another one of those as well.
Cards like Doubling Season, Winding Constrictor and Hardened Scales can increase the number of counters given by Proliferate, if this is something your friend wants to do and they're legal in the format you play.
This is more relevant when targeting players, especially in formats like Commander, who may have -1/-1 counters, energy counters or experience counters simultaneously; it's rare for other permanents to have more than one kind of counter on them (I believe this is by design, as otherwise it gets confusing).