Most particles that have ever been modeled Two billiard balls collide. Consider the two balls only, how many particles are in that system?
Have particle systems of that size been modeled with each individual particle before?
What is the largest object ever been modeled with pure particle physics?
 A: The biggest I know of is the Bolshoi simulation of cosmological structure formation. This used 8 billion particles - more superlatives are available on their web site.
This is a classical simulation i.e. the particles behave classically. If you're asking about quantum mechanical simulations then the answer is rather variable. Fully ab initio calculations are only feasible for relatively small molecules. Larger scale calculations, like protein structure, use approximations that render the calculation partly quantum and partly classical. So the largest size answer will depend on what approximations you're willing to accept.
A: From your comment to John's answer I see that you have a totally different vocabulary.

Two billiard balls collide. Consider the two balls only, how many particles are in that system?

A physicist will solve the collision of two colliding billiard balls by using the momenta and energies and taking the center of mass of each ball as a point particle. Rotational dynamics of the balls will enter in a more detailed calculation, but it will always be "two particles".
Now each billiard ball is composed out of an enormous number of mollecules tied up with electromagnetic forces in a stable configuration. The number is of the order of 10^23 molecules each. Each molecule is composed of a multiple of these, electrons and nucleons, and each nucleon is composed of three quarks. So the number of elementary particles is enormous, but not necessary to explain the macroscopic behavior of the billiard balls, at the energies that billiard balls collide. The model of mass(containing all those particles) and the motions of the center of mass and at most the rotational behavior is sufficient. 

Have particle systems of that size been modeled with each individual particle before?

It is not necessary to know what the molecules are doing to predict the trajectory of these two billiard balls to great accuracy, so no, nobody undertakes futile  tasks.

What is the largest object ever been modeled with pure particle physics?

The DNA molecule and now the nano particle studies deal with pure particle physics as it collectively impacts  into the macroscopic world.  I have not heard of scattering DNA molecules, and I doubt a model exists. Some form of scattering modeling must be necessary to get their collective interactions of nano particles so the number is the number of molecules in a nano particle. They seem to be of the order of hundreds or thousands.
