I had prepared the material below before I received your criteria.
As you know, each step in a reaction mechanism is an elementary step. Each step is characterized by its molecularity. A step could be unimolecular, as in
A → B or A → B + C
It could be bimolecular as in
2A → B + C or A + B → C + D
Or it could be trimolecular as in
3A → products or A + 2B → products or A + B + C → products
In a unimolecular reaction, the A molecule gains so much energy from collisions that it eventually falls apart.
In a bimolecular reaction, two molecules must collide with the correct orientation and sufficient energy for the reaction to take place.
In a trimolecular reaction, three molecules must collide simultaneously with the correct orientation and energy. This is an extremely rare occurrence.
Consider the elementary reaction A + 2B → products. Remember that molecules are extremely small particles with lots of empty space between them. For example, visualize 10 red marbles and 20 blue marbles moving around on the surface of a perfectly smooth skating rink, colliding elastically with each other and with the sides of the rink. There will be relatively few collisions between even any two marbles. The probability of three marbles colliding simultaneously is not zero, but it is extremely small. So we can ignore trimolecular collisions when we propose a mechanism. Even your solution proposed a trimolecular and even a tetramolecular step.
There are also some other points to remember:
1. Any reactant that does not appear in the rate determining step must be involved only after the rate determining step.
2. If the rate law is higher than second order, there are probably one or more equilibria occurring before the rate determining step.
We also have the added