Consider the following scenario: A trainer is trying to catch a rare or strong Pokemon, and figures that catching it in a PokeBall will have a low likelihood of actually catching and containing it.
What would happen if, after the trainer threw the first PokeBall and before the wild Pokemon breaks free, the trainer hit the occupied PokeBall with a second PokeBall? Would the both the original PokeBall and the wild Pokemon be "caught" by the second PokeBall? Would the wild Pokemon just be transferred from the first PokeBall to the second PokeBall? Would this double the likelihood that the Pokemon will be caught, due to the fact that it has to break out of two balls instead of one?
If the PokeBalls can be "layered," and the probability that you catch a Pokemon increases with how many PokeBalls you can layer on it, could you not just keep layering PokeBalls until you reach the strength of a Great or Ultra Ball?
We already know that inanimate objects and things other than Pokemon can be "caught" by PokeBalls, as evidenced by this question.