Is there any bigger supercharger you can put on a 2003 jaguar str? and if not how can I make it whine?

 

I know little about the STR other than it has the 4.2 litre V8 with the Eaton M112 supercharger.
I don't know if you can fit a bigger supercharger but I doubt it, but I suspect you can get a lot more SC whine by swapping out the stock air filter, filter box and intake plumbing for a cone filter set-up.
I know this works for the later AJ133 5.0 SC and AJ126 3.0 SC (XF, F-Type etc) although they both have later generation Eaton TVS superchargers and twin intake snorkels and air filters as opposed to single snorkels and filters as in the STR.
I put the Mina Gallery lower intake set up on my V6 F-Type and it increased the SC whine by a lot and Mina have an intake kit for the STR, see here: https://minagallery.com/jaguar-s-typ...-models-mkiii/
Mina also do a supercharger pulley upgrade (smaller pulley = more boost) for the STR, see here: https://minagallery.com/jaguar-s-typ...ulley-upgrade/

 

@2003JagStr, how many kilometres/miles are on the vehicle?

 

There is a twin screw upgrade for sale in the marketplace forum. That is a good as it gets

 

It's an old and somewhat out of date blower these days. Yes you can add a pulley and in the days past there were people changing the internal gearing to generate additional boost. Neither of these worked very well because of the limitations of the Eaton M112 blower. It's also known as a Heaton blower because everything you do to increase boost increases the intake air temperature even more. So you get stuck in a downward spiral of heat soak and restricted performance.

Yes you can get a lot more whine by messing with the air box and intake system. This is the same blower as the Ford Lightning trucks used and those guys really liked blower whine! So open up that intake tract for more noise!
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As club says it is past its prime for sure. More intake air coupled with a pulley and free flowing exhaust is the easiest i think. Adding more cooling for the air charge is very helpful. Either by an upgraded intercooler radiator or water meth injection or both. Those options get pricey but keep your same supercharger

 

it has 150k

 

You are very much stuck with what you have regarding the blower on the STR.
As mentioned above you can make them spin faster. This will give you noticeable improvement in lower RPM's, but as soon as you push the throttle down and it changes down the gears the improvement is minimal as the physical restrictions in the blower result in max air flow some time before you get to max rpm, even in standard form. So more whine but that is about it!
As is mentioned also the more air you push through the blower hotter the air gets. Much hotter in fact! This restricts any extra performance or efficiency you may get by pushing more air through.

Mellow