Good luck with this when it comes to R3 exhausts nothing is cheap .
My bike came to me with a decat pipe fitted I would suggest this is good place to start to free up more power and noise .
I looked for a set of 3 pipe TOR'S ( "Triumph off road" a factory performance parts made by Triumph in case you did not know ) ) these are long since out of production after months of searching I found nothing .
However the 3 mufflers are very heavy and worth getting shot of as it makes the bike feels much lighter without them .
If your not to worried about replacing the headers I would suggest DAP PERFORMANCE made in the UK and sold on EBay.
TRIUMPH ROCKET 3 SHORT CUSTOM TWIN SILENCERS and CAT REPLACEMENT | eBay
I had a set of these and they are plenty loud look good and very well made to be honest .
They do a couple of different pipes so have a look at there other stuff .
If you want headers I think its CES .VIKING , CARPENTER , ZARD ,or JARDINE not sure they are all still in production ( I know Jardine's aren't ) there all good but not cheap also I think TTS do larger bore standard looking header .
There must be others but that's all I know of .