Mind you, I am not implieing that the Harrier could be an air superiority fighter, it doesn't have the radar, but it is obviosley capable of defending itself in a classic (visual) dogfight. The Brit. pilots used it's thrust vectoring to out turn the super sonic French built Super Etenards that the Argentines used. Most dogfights take place at subsonic speeds, which is where the Harrier operates.
There is a difference between a multi role fighter and an air superiority fighter. Mainly radar and weapons, but performance can be affected. Case in point; an old friend of mine was a F-16 driver at Nellis AFB and part of the Aggressor Squadron. He said that when the F-15s were allowed to use their radars as designed the F-16s didn't stand a chance, but when the F-16s were allowed to get in close in a eyeball to eyeball dogfight, they humbled the F-15 drivers. In a classic dogfight the ability to out turn, accellerate, climb, dive, and use a gun trumps long range radar, speed, and missles. In the air superiority campaign everything is reversed; shoot them down before they know your there.