I work on corporate jet aircraft and perform troubleshooting, testing, and certification on pitot-static systems.
The reason aircraft have static ports for each pitot static system is to equalize or average out the small differences in static pressure caused by crosswinds when the aircraft is in flight. The difference in pressure caused by crosswind components on the static systems is not in the psi range, rather it is in the millibar or 1/10 of inches of mercury (inHg) range.
14CFR, Part 43, Appendix E, Table IV "Pressure-Altitude Difference" lists several baro-scale test points and associated altimeter readings used when certifying the altimeters. From the chart you can get an idea of how a difference of 1/10 in-HG will case a change of 90 to 100 ft in the altimeter reading (you can Google this table yourself).
An aircraft could easily have a difference in barometric pressure between the up-wind and down-wind sides of the aircraft when flying in a crosswind and this would cause an error of 100 ft or more on the altimeter reading if there was only a single static port located on one side of the aircraft.
On large aircraft which require 2 pilots, there are two completely separate pitot and static systems for each of the flight crew. Each pilot's instrument panel has its own altimeter and airspeed indicator (or air data computer) and display of altitude and airspeed information. There is a single pitot tube for each crewmember's instrumentation located on his side of the aircraft, but each crewmember's static system has two ports, one on each side of the fuselage which reduces the error effects of crosswind on the altimeter (static) systems (total of 4 static ports).
For peace of mind and safety, the flight crews continually compare (cross-check) each other's altimeter readings and if they see an error of 80 ft or more between the two systems they have an uneasy uncertainty about which altitude is correct and they will bring it to the mechanic's attention.
A blocked static port is a funny thing to troubleshoot, because a flight crew will say they saw a big altitude difference on one leg of the trip, then the next couple legs it was fine, then it had a split again. Next crew will fly and say there were no problems, followed by another crew complaining about splits. If you question the crews and ask if they were experiencing heavy crosswinds when they had the split they will say, "hmm, now that you mention it... yeah, we had some heavy crosswinds".
We then connect our pitot-static tester to each side's pitot tube and one of each side's static port, block off the opposite static port, and bring the airspeed and altitude up on the tester. What we are looking for when we connect the tester to the obstructed static port is a split between the captain's and first officer's altitudes. (Actually the obstructed side will start to wind the Airspeed indicator up really fast and can damage it if you don't stop the test quick enough).
One side is obstructed and the difference in static pressure caused by the crosswind is throwing off the altitude reading on one of the altimeters.
Two ports per system is to reduce errors in the altitude indication.