Corporate jet Captain reported a near miss on final approach; then another near miss from another aircraft entering the non-towered AUO airport traffic pattern. The Captain maneuvered from each near miss to avoid a collision.

Narrative

It is very commonplace at the AUO airport to have to sequence visually into an active pattern with 5+ training aircraft utilizing exactly the same runway. As a corporate operator we try to do all in our power to follow right of way rules and common courtesy in a pattern. Aircraft Y turning base in front of us; but we had to execute a go around due to them landing long as well as holding short of the intersecting runway. On our go-around; we then had to take evasive action for Aircraft Z on 45 as we were making our crosswind turn. As we continued on downwind I personally watched as another aircraft turned base effectively on top of another aircraft on final. The only analogy that comes to mind in this airspace is RODEO. There was also a King air in pattern on a extended final; but I had no time to catch his tail number as I had to concentrate on flying as slow as safely possible and sequence myself in this chaotic pattern.I am adamant that this airspace is in desperate need of a tower. Someone will die here if it is delayed much longer. Training ops are increasing this year; and GA as a whole is growing. There is a very real saturation point that this airspace is reaching. I strongly feel that it is not a matter of if; but when an accident will happen.As obvious solution to the obviously dangerous density is a control tower. Students and young instructors are being saturated with very real ATC duties in an uncontrolled environment that are beyond the scope of a normal uncontrolled field; much less a raining environment. compounded are the operations of standard GA and corporate aircraft. A secondary solution is to divide the pattern ops to IFR approaches local; and traffic pattern to ALX and CSG. If they continue to over-saturated pattern (likely due to cost savings in dispatch time) I am certain an event will happen.