When I see what looks like spam by a new user I go check out their other answers. Very often they all promote the same product or service. In the early days I would only flag one such answer but discovered that their other answers would sometimes remain intact, so these days I flag each answer.
Rather than flag each answer it would be better if the user account could be flagged. Because we only have 5 spam/offensive flags per day they can be very quickly used up on a bad day. I know we can still flag for moderator attention once we've used up out daily spam flags but I also think there is advantage in the moderators' attention being drawn to the user, where it will be more obvious that there are a multiple answers that need attention. Oddly enough, I nearly always see 3 per spammer.