Comes down to definitions of words: same "system" (by which you mean wave function) vs same particle. See bubble chamber: particle interacts with several atoms along a trajectory. Sure, you can claim "the wave function has collapsed after the first interaction", so it's "not the same system"...but then you're just saying that measurement affects the wave function...well, yeah, it does. Or you can say that the bubble chamber "is just a series of filters"...ok sure, everything that happens is just a series of filters, with sufficiently broad interpretation of that phrase.
> You appear to have completely missed the point. The path-length difference in the experiment I pointed you to is orders of magnitude larger than the standard two-slit experiment. That matters.
Seriously? I explained in detail what will happen in your proposed experiment as a function of path length and why the explanation comes down to the same thing as with the double slit. You completely ignored this, and then say that I completely missed the point...I honestly find your behaviour quite rude.