Isn't it per turn -with 3 rounds in a turn?
(there are 3 rounds
of player actions. In
every round, each
player performs 1
action, starting with
the First Player and
around the table)
from another player's summary
Technically you are correct. But the terms round and turn are often misused. I am sure he was talking about three rounds of actions per turn.
And the answer to the original question is still - "Yes, you can upgrade 3 times or draw 3 cards, or even urbanize 3 cities if you like."
But in reality other than 3 builds to complete a major line, or 3 deliveries at the end of the game are very unlikely to happen.