Copy Paste theory
(Note that the J-spec wastegate on the first turbo is smaller in diameter then the export Mkiv TT which has a 30mm wastegate.)
What size exhaust pipe diameter should I install?
If you have an NA then I would use a mandrel bent (bends where the pipe diameter is maintained) 2½" (65mm) system and I would use a 3" (75mm) to 3½" (90mm) system on the TT depending on how loud you want the car to be. Also with the TT you have to consider how much backpressure you have in the rest of your exhaust system, as too little backpressure will allow the boost to run away. This can happen because the single wastegate on the #1 turbo is not large enough by itself to control boost pressure but relies on exhaust backpressure to help keep the boost under control.
What's all this talk about downpipes on the TT?
The downpipe is considered to be approx. the first 3ft (1m) of exhaust pipe straight after the turbos. On the stock mkiv, this includes the first cat. The size of the downpipe diameter determines to a large extent how much backpressure your exhaust system can generate. Have this pipe too large and you will get runaway boost. Around 3" diameter is generally the maximum you can get away with on a TT but it does depend on whether you have any cats in the exhaust system.
What should I do about the Cats?
If you are legally allowed to, then you will get the best performance by removing them entirely. If you have to legally have them, then install high flow cats that match your exhaust pipe diameter. However, I have heard of people who "gut" the cats out making them into a straight pipe on the inside. This would not be easy on the mkiv Supra as the material inside the cats is pretty strong and would require alot of chiseling to get it out and you would then have trouble passing emmision controls with them removed.
Which muffler size and type is best?
A straight through muffler generally gives the least backpressure and hence the best power for your car. I use a 3½" In-Out Borla muffler on my TT 6 speed with a 3½" exhaust system. A slight variation on this is the Flow Master muffler which splits the exhaust flow with a high airflow divider and then rejoins it at the rear of the muffler. This design also offers minimal backpressure. Also, the muffler inlet and exhaust pipe sizes should match the diameter of your exhaust piping for best results. To reduce droning from the exhaust system you will need a resonator (with the same inlet and outlet diameter as your exhaust system) installed as well. The resonator is a small straight through muffer, usually installed half way between the engine and the tailpipe.
Should I remove the stock dual exhaust pipes before the muffler?
There is no flow advantages from maintaining the dual factory setup and if you are installing a complete new exhaust system then I would definitely remove them. They only add extra weight and complexity to the exhaust system.
PS Check the TRD High Response exhaust,produces a nice sound but not to loud