I am fairly confident that most companies with assemblies containing 2 or more axles on a chassis are NOT using family tables at the top level. 
If your assembly is not going to have any other components than the ones listed than family table may be a good solution.
Another alternative is to use the gathering assembly/150% overloaded approach with coordinate systems. Create one assembly for the tires where a common interface is defined(center axis of wheel and mating surface at hub). Add the tire to this assembly and other tires to the same coordinate system and use simp reps for each variant of wheel. Now create another assembly called chassis and add your plates to it(create simp reps for each variant). At this point you have two assemblies to maintain and control your "orderable components". Now you need placement control between the systems. Create a top level assembly called wheels_n_chassis. I see your plate as the backbone to which all other components will assemble to. Basically it can have one locator coordinate system. As an example define the bottom surface at center and middle of the plate as "Home Base". I prefer location control to be in the highest level assembly. There are many options at this point to locate tires and turn them on using simplified reps. You can use a skeleton with coordinate systems or add coordinate systems representing the tire location directly to the top level assembly. After assembling the tires to the proper combinations the setup is complete. I know this is a lot of upfront work, but the value of having position controlled in one location while minimizing the number of assemblies containing the orderable parts is very valuable. You can have an infinite number of tires managed in one assembly. As a bonus, use the feature name column to define the conditions of use for each wheel in the top level assembly as this will make it easier to manage simp reps.
