Here's a picture of the exhaust I removed.
Thank you. I took the liberty to edit your picture and added a few comments.
Please also refer to the attached .PDF.
EDIT: As far as understand it, the thingies in the middle of the exhaust which are suggested to be secondary cats in various posts could be in fact the main cats. Whether they are in use on all model years, and for all markets is unclear. They could be with the design of catalytic converters with ceramic core, but the function of resonators (or silencers). The parts catalog refers to those sections as "exhaust pipes" and provides no specifics.
StarTek from which the attached printout was originated has no information and only identifies the TWC close to the engine.
There are two O2S (oxygen sensors) upstream the TWC, which are used for fueling. If their are faulty, your air-fuel mixture will not be right.
The second pair of O2S are monitors. They are for the US market and a primary source of Check Engine Light/. Their function is ONLY to measure the health of the converters.
To me, it makes no sense to have another pair of converters this far out and AFTER the monitor O2Ss.
As of cats failure -- wrong fuel mixture (rich) will cause the cats to heat up 900°C and glow. The matrix inside melts and blocks the flow. Debris from the melted converter usually end up blown downstream and get stuck in the middle resonators (the cause of rattle and funny noises).
I hope this makes sense.
PS On an OBD-I car, as Peter's, one can run straight pipes and will have no problems.
On an OBD-II car such as yours, you can't fool the ECU.